diff --git "a/remarkable_lines/bisector/bisector_tasks.jsonl" "b/remarkable_lines/bisector/bisector_tasks.jsonl"
new file mode 100644--- /dev/null
+++ "b/remarkable_lines/bisector/bisector_tasks.jsonl"
@@ -0,0 +1,100 @@
+{"qid": 8100, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-3, 2], "B": [12, 5], "C": [1, -19]}, "answer": {"point": [7.411877251292977, -5.010449633542597]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 2), B=(12, 5), C=(1, -19); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08100_bisector.png", "im_dots_path": "/images/task_08100_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [7.411877251292977, -5.010449633542597]}, "choices": null, "image_choices": null}
+{"qid": 8101, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [14, 3], "B": [7, 2], "C": [1, -4]}, "answer": {"point": [5.057033389674803, 0.05703338967480343]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(14, 3), B=(7, 2), C=(1, -4); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08101_bisector.png", "im_dots_path": "/images/task_08101_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [5.057033389674803, 0.05703338967480343]}, "choices": null, "image_choices": null}
+{"qid": 8102, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [2, 20], "B": [-16, -2], "C": [-17, 20]}, "answer": {"point": [-16.599370301264045, 11.18614662780898]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, 20), B=(-16, -2), C=(-17, 20); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08102_bisector.png", "im_dots_path": "/images/task_08102_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-16.599370301264045, 11.18614662780898]}, "choices": null, "image_choices": null}
+{"qid": 8103, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-13, 15], "B": [-18, -19], "C": [-13, -20]}, "answer": {"point": [-13.0, -15.47784012887197]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-13, 15), B=(-18, -19), C=(-13, -20); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08103_bisector.png", "im_dots_path": "/images/task_08103_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-13.0, -15.47784012887197]}, "choices": null, "image_choices": null}
+{"qid": 8104, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-12, 19], "B": [14, 17], "C": [-10, -9]}, "answer": {"point": [2.4420158044080775, 4.478850454775419]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-12, 19), B=(14, 17), C=(-10, -9); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08104_bisector.png", "im_dots_path": "/images/task_08104_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [2.4420158044080775, 4.478850454775419]}, "choices": null, "image_choices": null}
+{"qid": 8105, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [18, -9], "B": [-7, 1], "C": [12, 2]}, "answer": {"point": [8.073313963358222, -5.029325585343289]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(18, -9), B=(-7, 1), C=(12, 2); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08105_bisector.png", "im_dots_path": "/images/task_08105_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [8.073313963358222, -5.029325585343289]}, "choices": null, "image_choices": null}
+{"qid": 8106, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [2, -3], "B": [-14, -16], "C": [4, 19]}, "answer": {"point": [-5.310885294449142, 0.8955008163488914]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -3), B=(-14, -16), C=(4, 19); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08106_bisector.png", "im_dots_path": "/images/task_08106_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-5.310885294449142, 0.8955008163488914]}, "choices": null, "image_choices": null}
+{"qid": 8107, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [16, 8], "B": [-2, 10], "C": [-16, 3]}, "answer": {"point": [3.864700126223823, 9.348366652641799]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(16, 8), B=(-2, 10), C=(-16, 3); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08107_bisector.png", "im_dots_path": "/images/task_08107_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [3.864700126223823, 9.348366652641799]}, "choices": null, "image_choices": null}
+{"qid": 8108, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [4, 5], "B": [2, 14], "C": [-7, -2]}, "answer": {"point": [-1.7279220613578554, 7.3725830020304794]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 5), B=(2, 14), C=(-7, -2); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08108_bisector.png", "im_dots_path": "/images/task_08108_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-1.7279220613578554, 7.3725830020304794]}, "choices": null, "image_choices": null}
+{"qid": 8109, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [4, 1], "B": [1, 4], "C": [-20, -2]}, "answer": {"point": [0.09617405130023561, 0.5120217564125294]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 1), B=(1, 4), C=(-20, -2); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08109_bisector.png", "im_dots_path": "/images/task_08109_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [0.09617405130023561, 0.5120217564125294]}, "choices": null, "image_choices": null}
+{"qid": 8110, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-3, 15], "B": [1, -3], "C": [-19, -18]}, "answer": {"point": [-0.6214224502478467, 4.29640102611531]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 15), B=(1, -3), C=(-19, -18); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08110_bisector.png", "im_dots_path": "/images/task_08110_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-0.6214224502478467, 4.29640102611531]}, "choices": null, "image_choices": null}
+{"qid": 8111, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-5, -16], "B": [-14, -15], "C": [18, -9]}, "answer": {"point": [0.005015893913110323, -14.476734293156879]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, -16), B=(-14, -15), C=(18, -9); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08111_bisector.png", "im_dots_path": "/images/task_08111_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [0.005015893913110323, -14.476734293156879]}, "choices": null, "image_choices": null}
+{"qid": 8112, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [18, -1], "B": [-8, 17], "C": [20, -11]}, "answer": {"point": [18.88802136408409, -5.4401068204204615]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(18, -1), B=(-8, 17), C=(20, -11); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08112_bisector.png", "im_dots_path": "/images/task_08112_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [18.88802136408409, -5.4401068204204615]}, "choices": null, "image_choices": null}
+{"qid": 8113, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-1, -15], "B": [-18, -4], "C": [-14, -8]}, "answer": {"point": [-11.161234416453066, -9.528566083448348]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -15), B=(-18, -4), C=(-14, -8); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08113_bisector.png", "im_dots_path": "/images/task_08113_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-11.161234416453066, -9.528566083448348]}, "choices": null, "image_choices": null}
+{"qid": 8114, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [8, 2], "B": [-5, -14], "C": [0, 14]}, "answer": {"point": [-2.05809619692097, 2.4746612972425672]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, 2), B=(-5, -14), C=(0, 14); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08114_bisector.png", "im_dots_path": "/images/task_08114_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-2.05809619692097, 2.4746612972425672]}, "choices": null, "image_choices": null}
+{"qid": 8115, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-10, 14], "B": [-17, 4], "C": [-20, -6]}, "answer": {"point": [-15.3899544884192, 3.2200910231616047]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 14), B=(-17, 4), C=(-20, -6); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08115_bisector.png", "im_dots_path": "/images/task_08115_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-15.3899544884192, 3.2200910231616047]}, "choices": null, "image_choices": null}
+{"qid": 8116, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-17, 9], "B": [-13, -6], "C": [20, 2]}, "answer": {"point": [-3.3668146028888737, -3.6646823279730603]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-17, 9), B=(-13, -6), C=(20, 2); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08116_bisector.png", "im_dots_path": "/images/task_08116_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-3.3668146028888737, -3.6646823279730603]}, "choices": null, "image_choices": null}
+{"qid": 8117, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [17, 6], "B": [-19, -5], "C": [19, 2]}, "answer": {"point": [17.986939353244413, 4.026121293511175]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(17, 6), B=(-19, -5), C=(19, 2); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08117_bisector.png", "im_dots_path": "/images/task_08117_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [17.986939353244413, 4.026121293511175]}, "choices": null, "image_choices": null}
+{"qid": 8118, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-18, -10], "B": [-8, 3], "C": [10, -16]}, "answer": {"point": [-12.775294585338468, -3.2078829609400086]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-18, -10), B=(-8, 3), C=(10, -16); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08118_bisector.png", "im_dots_path": "/images/task_08118_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-12.775294585338468, -3.2078829609400086]}, "choices": null, "image_choices": null}
+{"qid": 8119, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [6, 7], "B": [7, 11], "C": [-20, 4]}, "answer": {"point": [2.6516254384475504, 6.61364908905164]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 7), B=(7, 11), C=(-20, 4); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08119_bisector.png", "im_dots_path": "/images/task_08119_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [2.6516254384475504, 6.61364908905164]}, "choices": null, "image_choices": null}
+{"qid": 8120, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [2, 13], "B": [20, -13], "C": [0, 17]}, "answer": {"point": [3.9862599917089674, 10.130957789753714]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, 13), B=(20, -13), C=(0, 17); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08120_bisector.png", "im_dots_path": "/images/task_08120_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [3.9862599917089674, 10.130957789753714]}, "choices": null, "image_choices": null}
+{"qid": 8121, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [15, -7], "B": [3, 17], "C": [-17, 3]}, "answer": {"point": [-1.7554799819621505, -1.7639125056368279]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(15, -7), B=(3, 17), C=(-17, 3); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08121_bisector.png", "im_dots_path": "/images/task_08121_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-1.7554799819621505, -1.7639125056368279]}, "choices": null, "image_choices": null}
+{"qid": 8122, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-4, -1], "B": [-18, 6], "C": [14, 8]}, "answer": {"point": [1.904748349659259, 1.9523741748296295]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, -1), B=(-18, 6), C=(14, 8); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08122_bisector.png", "im_dots_path": "/images/task_08122_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [1.904748349659259, 1.9523741748296295]}, "choices": null, "image_choices": null}
+{"qid": 8123, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-3, 3], "B": [-5, 9], "C": [-17, -16]}, "answer": {"point": [-7.536128400534522, 3.716399165553079]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 3), B=(-5, 9), C=(-17, -16); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08123_bisector.png", "im_dots_path": "/images/task_08123_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-7.536128400534522, 3.716399165553079]}, "choices": null, "image_choices": null}
+{"qid": 8124, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [20, 10], "B": [8, -18], "C": [16, -4]}, "answer": {"point": [17.384446741654372, 0.8455635957902999]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(20, 10), B=(8, -18), C=(16, -4); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08124_bisector.png", "im_dots_path": "/images/task_08124_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [17.384446741654372, 0.8455635957902999]}, "choices": null, "image_choices": null}
+{"qid": 8125, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [4, -3], "B": [9, 2], "C": [-2, 18]}, "answer": {"point": [6.6468752302873995, -0.3531247697126]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -3), B=(9, 2), C=(-2, 18); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08125_bisector.png", "im_dots_path": "/images/task_08125_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [6.6468752302873995, -0.3531247697126]}, "choices": null, "image_choices": null}
+{"qid": 8126, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [1, -9], "B": [-7, 3], "C": [-5, 5]}, "answer": {"point": [-5.747095769390142, 1.1206436540852123]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, -9), B=(-7, 3), C=(-5, 5); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08126_bisector.png", "im_dots_path": "/images/task_08126_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-5.747095769390142, 1.1206436540852123]}, "choices": null, "image_choices": null}
+{"qid": 8127, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-2, 9], "B": [12, -4], "C": [-15, -13]}, "answer": {"point": [4.623314272750374, 2.849779603874652]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, 9), B=(12, -4), C=(-15, -13); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08127_bisector.png", "im_dots_path": "/images/task_08127_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [4.623314272750374, 2.849779603874652]}, "choices": null, "image_choices": null}
+{"qid": 8128, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-7, 0], "B": [-5, -15], "C": [0, -19]}, "answer": {"point": [-2.08126577988514, -13.350850026026047]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, 0), B=(-5, -15), C=(0, -19); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08128_bisector.png", "im_dots_path": "/images/task_08128_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-2.08126577988514, -13.350850026026047]}, "choices": null, "image_choices": null}
+{"qid": 8129, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-7, -1], "B": [-6, -19], "C": [12, -14]}, "answer": {"point": [2.3308068849410897, -7.384236289696534]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -1), B=(-6, -19), C=(12, -14); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08129_bisector.png", "im_dots_path": "/images/task_08129_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [2.3308068849410897, -7.384236289696534]}, "choices": null, "image_choices": null}
+{"qid": 8130, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-19, 20], "B": [-16, -10], "C": [2, -16]}, "answer": {"point": [-6.111161981867855, -2.0951508882265353]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-19, 20), B=(-16, -10), C=(2, -16); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08130_bisector.png", "im_dots_path": "/images/task_08130_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-6.111161981867855, -2.0951508882265353]}, "choices": null, "image_choices": null}
+{"qid": 8131, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [6, -9], "B": [-6, 6], "C": [8, 7]}, "answer": {"point": [7.155623323717491, 0.24498658973992352]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, -9), B=(-6, 6), C=(8, 7); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08131_bisector.png", "im_dots_path": "/images/task_08131_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [7.155623323717491, 0.24498658973992352]}, "choices": null, "image_choices": null}
+{"qid": 8132, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [4, -16], "B": [19, -17], "C": [-2, 8]}, "answer": {"point": [11.062260420919392, -7.5503100249040385]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -16), B=(19, -17), C=(-2, 8); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08132_bisector.png", "im_dots_path": "/images/task_08132_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [11.062260420919392, -7.5503100249040385]}, "choices": null, "image_choices": null}
+{"qid": 8133, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [8, 18], "B": [-8, 18], "C": [-13, 12]}, "answer": {"point": [-10.114146486096491, 15.46302421668421]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, 18), B=(-8, 18), C=(-13, 12); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08133_bisector.png", "im_dots_path": "/images/task_08133_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-10.114146486096491, 15.46302421668421]}, "choices": null, "image_choices": null}
+{"qid": 8134, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-10, 11], "B": [-19, 11], "C": [-4, 16]}, "answer": {"point": [-10.969185312369918, 13.676938229210029]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 11), B=(-19, 11), C=(-4, 16); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08134_bisector.png", "im_dots_path": "/images/task_08134_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-10.969185312369918, 13.676938229210029]}, "choices": null, "image_choices": null}
+{"qid": 8135, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-7, -19], "B": [-8, 15], "C": [20, -19]}, "answer": {"point": [-7.380038513178731, -6.078690551923153]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -19), B=(-8, 15), C=(20, -19); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08135_bisector.png", "im_dots_path": "/images/task_08135_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-7.380038513178731, -6.078690551923153]}, "choices": null, "image_choices": null}
+{"qid": 8136, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [4, -9], "B": [16, -9], "C": [-15, 10]}, "answer": {"point": [9.099539400917308, -9.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -9), B=(16, -9), C=(-15, 10); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08136_bisector.png", "im_dots_path": "/images/task_08136_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [9.099539400917308, -9.0]}, "choices": null, "image_choices": null}
+{"qid": 8137, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [18, 2], "B": [17, -16], "C": [18, -9]}, "answer": {"point": [18.0, -5.900980486407215]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(18, 2), B=(17, -16), C=(18, -9); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08137_bisector.png", "im_dots_path": "/images/task_08137_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [18.0, -5.900980486407215]}, "choices": null, "image_choices": null}
+{"qid": 8138, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [13, 5], "B": [14, 8], "C": [18, 15]}, "answer": {"point": [14.881924836846169, 9.543368464480796]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(13, 5), B=(14, 8), C=(18, 15); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08138_bisector.png", "im_dots_path": "/images/task_08138_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [14.881924836846169, 9.543368464480796]}, "choices": null, "image_choices": null}
+{"qid": 8139, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-19, 12], "B": [-12, -19], "C": [11, 16]}, "answer": {"point": [-6.056769710838225, 13.725764038554903]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-19, 12), B=(-12, -19), C=(11, 16); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08139_bisector.png", "im_dots_path": "/images/task_08139_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-6.056769710838225, 13.725764038554903]}, "choices": null, "image_choices": null}
+{"qid": 8140, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-5, -5], "B": [8, -11], "C": [20, -18]}, "answer": {"point": [7.688485057226288, -11.598012229757671]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, -5), B=(8, -11), C=(20, -18); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08140_bisector.png", "im_dots_path": "/images/task_08140_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [7.688485057226288, -11.598012229757671]}, "choices": null, "image_choices": null}
+{"qid": 8141, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [12, -19], "B": [-12, 13], "C": [9, -13]}, "answer": {"point": [10.365602468108523, -15.731204936217049]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(12, -19), B=(-12, 13), C=(9, -13); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08141_bisector.png", "im_dots_path": "/images/task_08141_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [10.365602468108523, -15.731204936217049]}, "choices": null, "image_choices": null}
+{"qid": 8142, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [2, -2], "B": [18, 7], "C": [-9, -13]}, "answer": {"point": [7.063406400049349, 0.8481661000277587]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -2), B=(18, 7), C=(-9, -13); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08142_bisector.png", "im_dots_path": "/images/task_08142_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [7.063406400049349, 0.8481661000277587]}, "choices": null, "image_choices": null}
+{"qid": 8143, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [6, -2], "B": [18, -17], "C": [-9, 2]}, "answer": {"point": [9.837921212319484, -6.797401515399355]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, -2), B=(18, -17), C=(-9, 2); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08143_bisector.png", "im_dots_path": "/images/task_08143_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [9.837921212319484, -6.797401515399355]}, "choices": null, "image_choices": null}
+{"qid": 8144, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [0, -7], "B": [-18, -4], "C": [2, 0]}, "answer": {"point": [-3.7035384966362264, -1.1407076993272454]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, -7), B=(-18, -4), C=(2, 0); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08144_bisector.png", "im_dots_path": "/images/task_08144_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-3.7035384966362264, -1.1407076993272454]}, "choices": null, "image_choices": null}
+{"qid": 8145, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [0, 16], "B": [6, 6], "C": [4, -11]}, "answer": {"point": [1.6208825047762203, 5.059043092760514]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 16), B=(6, 6), C=(4, -11); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08145_bisector.png", "im_dots_path": "/images/task_08145_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [1.6208825047762203, 5.059043092760514]}, "choices": null, "image_choices": null}
+{"qid": 8146, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-11, -9], "B": [-10, -4], "C": [11, 8]}, "answer": {"point": [-7.169527312299696, -6.040089286777039]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-11, -9), B=(-10, -4), C=(11, 8); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08146_bisector.png", "im_dots_path": "/images/task_08146_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-7.169527312299696, -6.040089286777039]}, "choices": null, "image_choices": null}
+{"qid": 8147, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [18, -19], "B": [0, -20], "C": [17, 17]}, "answer": {"point": [5.671031518241854, -7.6571666955912585]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(18, -19), B=(0, -20), C=(17, 17); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08147_bisector.png", "im_dots_path": "/images/task_08147_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [5.671031518241854, -7.6571666955912585]}, "choices": null, "image_choices": null}
+{"qid": 8148, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-20, 13], "B": [-16, -18], "C": [2, 17]}, "answer": {"point": [-18.550784303726704, 1.768578353881954]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-20, 13), B=(-16, -18), C=(2, 17); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08148_bisector.png", "im_dots_path": "/images/task_08148_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-18.550784303726704, 1.768578353881954]}, "choices": null, "image_choices": null}
+{"qid": 8149, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [7, 6], "B": [-15, 12], "C": [14, 17]}, "answer": {"point": [0.2453493158147019, 7.8421774593232625]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, 6), B=(-15, 12), C=(14, 17); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08149_bisector.png", "im_dots_path": "/images/task_08149_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [0.2453493158147019, 7.8421774593232625]}, "choices": null, "image_choices": null}
+{"qid": 8150, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [6, 16], "B": [17, 0], "C": [9, -16]}, "answer": {"point": [13.0667907008296, 5.721031707884216]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 16), B=(17, 0), C=(9, -16); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08150_bisector.png", "im_dots_path": "/images/task_08150_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [13.0667907008296, 5.721031707884216]}, "choices": null, "image_choices": null}
+{"qid": 8151, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-8, 9], "B": [18, 19], "C": [-13, -2]}, "answer": {"point": [-10.13298223345829, 4.307439086391768]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 9), B=(18, 19), C=(-13, -2); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08151_bisector.png", "im_dots_path": "/images/task_08151_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-10.13298223345829, 4.307439086391768]}, "choices": null, "image_choices": null}
+{"qid": 8152, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [16, -7], "B": [-19, 20], "C": [-2, 0]}, "answer": {"point": [-7.169058465909723, 6.0812452540114394]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(16, -7), B=(-19, 20), C=(-2, 0); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08152_bisector.png", "im_dots_path": "/images/task_08152_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-7.169058465909723, 6.0812452540114394]}, "choices": null, "image_choices": null}
+{"qid": 8153, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [19, 12], "B": [-7, 13], "C": [-9, -15]}, "answer": {"point": [5.5311388112258335, -0.9878304320322309]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(19, 12), B=(-7, 13), C=(-9, -15); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08153_bisector.png", "im_dots_path": "/images/task_08153_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [5.5311388112258335, -0.9878304320322309]}, "choices": null, "image_choices": null}
+{"qid": 8154, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-14, 2], "B": [-4, -19], "C": [19, 11]}, "answer": {"point": [5.309482838445459, -6.857196297679836]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-14, 2), B=(-4, -19), C=(19, 11); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08154_bisector.png", "im_dots_path": "/images/task_08154_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [5.309482838445459, -6.857196297679836]}, "choices": null, "image_choices": null}
+{"qid": 8155, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-7, -12], "B": [-14, 1], "C": [20, -2]}, "answer": {"point": [-2.474829002902897, -0.016926852685038487]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -12), B=(-14, 1), C=(20, -2); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08155_bisector.png", "im_dots_path": "/images/task_08155_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-2.474829002902897, -0.016926852685038487]}, "choices": null, "image_choices": null}
+{"qid": 8156, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-19, -13], "B": [20, -2], "C": [-1, 17]}, "answer": {"point": [2.553367585260377, -6.920845040054765]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-19, -13), B=(20, -2), C=(-1, 17); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08156_bisector.png", "im_dots_path": "/images/task_08156_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [2.553367585260377, -6.920845040054765]}, "choices": null, "image_choices": null}
+{"qid": 8157, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-5, -13], "B": [-12, 18], "C": [-13, 4]}, "answer": {"point": [-10.549219837554164, -1.207907845197401]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, -13), B=(-12, 18), C=(-13, 4); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08157_bisector.png", "im_dots_path": "/images/task_08157_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-10.549219837554164, -1.207907845197401]}, "choices": null, "image_choices": null}
+{"qid": 8158, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [5, -9], "B": [14, 0], "C": [-2, 10]}, "answer": {"point": [7.824465862001656, 3.8597088362489664]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, -9), B=(14, 0), C=(-2, 10); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08158_bisector.png", "im_dots_path": "/images/task_08158_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [7.824465862001656, 3.8597088362489664]}, "choices": null, "image_choices": null}
+{"qid": 8159, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [1, 6], "B": [-20, 2], "C": [5, -6]}, "answer": {"point": [2.7954388968539448, 0.6136833094381658]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, 6), B=(-20, 2), C=(5, -6); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08159_bisector.png", "im_dots_path": "/images/task_08159_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [2.7954388968539448, 0.6136833094381658]}, "choices": null, "image_choices": null}
+{"qid": 8160, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [7, -8], "B": [-15, -1], "C": [-11, -8]}, "answer": {"point": [-12.752387936883197, -4.933321110454405]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, -8), B=(-15, -1), C=(-11, -8); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08160_bisector.png", "im_dots_path": "/images/task_08160_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-12.752387936883197, -4.933321110454405]}, "choices": null, "image_choices": null}
+{"qid": 8161, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [9, 18], "B": [-18, 6], "C": [10, 15]}, "answer": {"point": [6.378777594041324, 16.835012264018363]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 18), B=(-18, 6), C=(10, 15); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08161_bisector.png", "im_dots_path": "/images/task_08161_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [6.378777594041324, 16.835012264018363]}, "choices": null, "image_choices": null}
+{"qid": 8162, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-3, 12], "B": [-11, 15], "C": [-11, 20]}, "answer": {"point": [-8.548074369326308, 14.080527888497366]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 12), B=(-11, 15), C=(-11, 20); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08162_bisector.png", "im_dots_path": "/images/task_08162_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-8.548074369326308, 14.080527888497366]}, "choices": null, "image_choices": null}
+{"qid": 8163, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-14, 13], "B": [6, 7], "C": [-17, -9]}, "answer": {"point": [-15.281059430645554, 3.6055641752659207]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-14, 13), B=(6, 7), C=(-17, -9); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08163_bisector.png", "im_dots_path": "/images/task_08163_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-15.281059430645554, 3.6055641752659207]}, "choices": null, "image_choices": null}
+{"qid": 8164, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-18, 16], "B": [-19, 5], "C": [-3, 18]}, "answer": {"point": [-18.423314029572094, 11.343545674706993]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-18, 16), B=(-19, 5), C=(-3, 18); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08164_bisector.png", "im_dots_path": "/images/task_08164_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-18.423314029572094, 11.343545674706993]}, "choices": null, "image_choices": null}
+{"qid": 8165, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-11, 10], "B": [19, 8], "C": [1, 10]}, "answer": {"point": [-3.5110240501610903, 10.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-11, 10), B=(19, 8), C=(1, 10); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08165_bisector.png", "im_dots_path": "/images/task_08165_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-3.5110240501610903, 10.0]}, "choices": null, "image_choices": null}
+{"qid": 8166, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-14, -12], "B": [-10, -3], "C": [-2, -7]}, "answer": {"point": [-11.630361115954564, -6.6683125108977706]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-14, -12), B=(-10, -3), C=(-2, -7); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08166_bisector.png", "im_dots_path": "/images/task_08166_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-11.630361115954564, -6.6683125108977706]}, "choices": null, "image_choices": null}
+{"qid": 8167, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [3, 19], "B": [14, 9], "C": [-10, 3]}, "answer": {"point": [-1.8796956298343983, 12.994220763280738]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(3, 19), B=(14, 9), C=(-10, 3); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08167_bisector.png", "im_dots_path": "/images/task_08167_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-1.8796956298343983, 12.994220763280738]}, "choices": null, "image_choices": null}
+{"qid": 8168, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-5, 15], "B": [-17, -3], "C": [2, -16]}, "answer": {"point": [-1.6088225344013163, -0.018071633365598586]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 15), B=(-17, -3), C=(2, -16); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08168_bisector.png", "im_dots_path": "/images/task_08168_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-1.6088225344013163, -0.018071633365598586]}, "choices": null, "image_choices": null}
+{"qid": 8169, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-5, 16], "B": [1, 13], "C": [4, -15]}, "answer": {"point": [1.51617148202033, 8.182399501143584]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 16), B=(1, 13), C=(4, -15); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08169_bisector.png", "im_dots_path": "/images/task_08169_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [1.51617148202033, 8.182399501143584]}, "choices": null, "image_choices": null}
+{"qid": 8170, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-7, 12], "B": [-16, 11], "C": [3, 5]}, "answer": {"point": [-3.8753247407603224, 9.812727318532227]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, 12), B=(-16, 11), C=(3, 5); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08170_bisector.png", "im_dots_path": "/images/task_08170_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-3.8753247407603224, 9.812727318532227]}, "choices": null, "image_choices": null}
+{"qid": 8171, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [19, 6], "B": [-2, 11], "C": [-1, 0]}, "answer": {"point": [-1.4916828434004246, 5.408511277404671]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(19, 6), B=(-2, 11), C=(-1, 0); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08171_bisector.png", "im_dots_path": "/images/task_08171_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-1.4916828434004246, 5.408511277404671]}, "choices": null, "image_choices": null}
+{"qid": 8172, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-5, 2], "B": [17, 10], "C": [9, 16]}, "answer": {"point": [9.617199410585162, 7.315345240212786]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 2), B=(17, 10), C=(9, 16); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08172_bisector.png", "im_dots_path": "/images/task_08172_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [9.617199410585162, 7.315345240212786]}, "choices": null, "image_choices": null}
+{"qid": 8173, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [11, -11], "B": [9, -15], "C": [-7, 2]}, "answer": {"point": [6.317631029227863, -12.149982968554607]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(11, -11), B=(9, -15), C=(-7, 2); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08173_bisector.png", "im_dots_path": "/images/task_08173_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [6.317631029227863, -12.149982968554607]}, "choices": null, "image_choices": null}
+{"qid": 8174, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-15, 0], "B": [-10, 2], "C": [-4, 9]}, "answer": {"point": [-11.967279771042632, 1.213088091582948]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-15, 0), B=(-10, 2), C=(-4, 9); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08174_bisector.png", "im_dots_path": "/images/task_08174_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-11.967279771042632, 1.213088091582948]}, "choices": null, "image_choices": null}
+{"qid": 8175, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-19, 17], "B": [1, -1], "C": [-8, -18]}, "answer": {"point": [-12.585547351609039, -3.40962206306215]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-19, 17), B=(1, -1), C=(-8, -18); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08175_bisector.png", "im_dots_path": "/images/task_08175_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-12.585547351609039, -3.40962206306215]}, "choices": null, "image_choices": null}
+{"qid": 8176, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [20, 9], "B": [17, -10], "C": [14, -17]}, "answer": {"point": [15.74329767903037, -12.932305415595808]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(20, 9), B=(17, -10), C=(14, -17); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08176_bisector.png", "im_dots_path": "/images/task_08176_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [15.74329767903037, -12.932305415595808]}, "choices": null, "image_choices": null}
+{"qid": 8177, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-17, -7], "B": [-5, -17], "C": [10, 5]}, "answer": {"point": [0.18757306980538574, -9.391559497618768]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-17, -7), B=(-5, -17), C=(10, 5); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08177_bisector.png", "im_dots_path": "/images/task_08177_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [0.18757306980538574, -9.391559497618768]}, "choices": null, "image_choices": null}
+{"qid": 8178, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-9, 11], "B": [16, 17], "C": [0, -12]}, "answer": {"point": [-5.066875727951595, 0.9486824158762971]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 11), B=(16, 17), C=(0, -12); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08178_bisector.png", "im_dots_path": "/images/task_08178_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-5.066875727951595, 0.9486824158762971]}, "choices": null, "image_choices": null}
+{"qid": 8179, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [17, 15], "B": [-16, 9], "C": [3, 0]}, "answer": {"point": [8.39419295721267, 5.779492454156432]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(17, 15), B=(-16, 9), C=(3, 0); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08179_bisector.png", "im_dots_path": "/images/task_08179_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [8.39419295721267, 5.779492454156432]}, "choices": null, "image_choices": null}
+{"qid": 8180, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-10, 11], "B": [0, 10], "C": [-12, -12]}, "answer": {"point": [-3.6394276594710986, 3.3277159576363187]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 11), B=(0, 10), C=(-12, -12); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08180_bisector.png", "im_dots_path": "/images/task_08180_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-3.6394276594710986, 3.3277159576363187]}, "choices": null, "image_choices": null}
+{"qid": 8181, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-19, -13], "B": [2, -16], "C": [-11, -5]}, "answer": {"point": [-14.562391868188445, -8.562391868188444]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-19, -13), B=(2, -16), C=(-11, -5); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08181_bisector.png", "im_dots_path": "/images/task_08181_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-14.562391868188445, -8.562391868188444]}, "choices": null, "image_choices": null}
+{"qid": 8182, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [3, -7], "B": [-18, -19], "C": [3, 18]}, "answer": {"point": [-4.772700215604877, -11.441542980345645]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(3, -7), B=(-18, -19), C=(3, 18); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08182_bisector.png", "im_dots_path": "/images/task_08182_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-4.772700215604877, -11.441542980345645]}, "choices": null, "image_choices": null}
+{"qid": 8183, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [8, -10], "B": [-10, 6], "C": [-11, 13]}, "answer": {"point": [-10.44667934795949, 9.12675543571644]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, -10), B=(-10, 6), C=(-11, 13); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08183_bisector.png", "im_dots_path": "/images/task_08183_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-10.44667934795949, 9.12675543571644]}, "choices": null, "image_choices": null}
+{"qid": 8184, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-12, -11], "B": [0, 13], "C": [20, -15]}, "answer": {"point": [9.083269131959842, 0.2834232152562243]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-12, -11), B=(0, 13), C=(20, -15); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08184_bisector.png", "im_dots_path": "/images/task_08184_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [9.083269131959842, 0.2834232152562243]}, "choices": null, "image_choices": null}
+{"qid": 8185, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [20, 9], "B": [-18, 4], "C": [-2, 5]}, "answer": {"point": [-2.132424979462799, 6.087838818491737]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(20, 9), B=(-18, 4), C=(-2, 5); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08185_bisector.png", "im_dots_path": "/images/task_08185_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-2.132424979462799, 6.087838818491737]}, "choices": null, "image_choices": null}
+{"qid": 8186, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-1, -14], "B": [16, 14], "C": [19, 3]}, "answer": {"point": [13.835978776014247, -1.3894180403878882]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -14), B=(16, 14), C=(19, 3); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08186_bisector.png", "im_dots_path": "/images/task_08186_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [13.835978776014247, -1.3894180403878882]}, "choices": null, "image_choices": null}
+{"qid": 8187, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [11, 11], "B": [1, 13], "C": [10, 13]}, "answer": {"point": [10.468797880203049, 12.062404239593903]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(11, 11), B=(1, 13), C=(10, 13); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08187_bisector.png", "im_dots_path": "/images/task_08187_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [10.468797880203049, 12.062404239593903]}, "choices": null, "image_choices": null}
+{"qid": 8188, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [12, 9], "B": [-19, -11], "C": [1, 20]}, "answer": {"point": [-4.932094517833881, 10.805253497357485]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(12, 9), B=(-19, -11), C=(1, 20); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08188_bisector.png", "im_dots_path": "/images/task_08188_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-4.932094517833881, 10.805253497357485]}, "choices": null, "image_choices": null}
+{"qid": 8189, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-20, 19], "B": [10, -17], "C": [-8, 2]}, "answer": {"point": [-2.4649784834958397, -3.842522711865503]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-20, 19), B=(10, -17), C=(-8, 2); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08189_bisector.png", "im_dots_path": "/images/task_08189_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-2.4649784834958397, -3.842522711865503]}, "choices": null, "image_choices": null}
+{"qid": 8190, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-17, 3], "B": [11, 10], "C": [-9, 17]}, "answer": {"point": [-1.8313590268533855, 14.490975659398686]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-17, 3), B=(11, 10), C=(-9, 17); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08190_bisector.png", "im_dots_path": "/images/task_08190_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-1.8313590268533855, 14.490975659398686]}, "choices": null, "image_choices": null}
+{"qid": 8191, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [16, 5], "B": [5, -7], "C": [15, -5]}, "answer": {"point": [10.540246057310593, -0.9560952102066258]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(16, 5), B=(5, -7), C=(15, -5); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08191_bisector.png", "im_dots_path": "/images/task_08191_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [10.540246057310593, -0.9560952102066258]}, "choices": null, "image_choices": null}
+{"qid": 8192, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [10, 10], "B": [-14, -9], "C": [-13, 16]}, "answer": {"point": [-1.6924934166587362, 0.7434427118118342]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, 10), B=(-14, -9), C=(-13, 16); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08192_bisector.png", "im_dots_path": "/images/task_08192_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [-1.6924934166587362, 0.7434427118118342]}, "choices": null, "image_choices": null}
+{"qid": 8193, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [16, -14], "B": [-19, -17], "C": [-12, -19]}, "answer": {"point": [-7.193337743224387, -18.14166745414721]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(16, -14), B=(-19, -17), C=(-12, -19); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08193_bisector.png", "im_dots_path": "/images/task_08193_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-7.193337743224387, -18.14166745414721]}, "choices": null, "image_choices": null}
+{"qid": 8194, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-1, -18], "B": [-13, 10], "C": [4, -19]}, "answer": {"point": [1.3770111268113219, -18.475402225362267]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -18), B=(-13, 10), C=(4, -19); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08194_bisector.png", "im_dots_path": "/images/task_08194_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [1.3770111268113219, -18.475402225362267]}, "choices": null, "image_choices": null}
+{"qid": 8195, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [12, 2], "B": [-2, 18], "C": [20, -8]}, "answer": {"point": [15.074569951240365, -1.8432124390504554]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(12, 2), B=(-2, 18), C=(20, -8); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08195_bisector.png", "im_dots_path": "/images/task_08195_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [15.074569951240365, -1.8432124390504554]}, "choices": null, "image_choices": null}
+{"qid": 8196, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-6, 20], "B": [14, 20], "C": [-13, -17]}, "answer": {"point": [3.0237763281123935, 20.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, 20), B=(14, 20), C=(-13, -17); find the intersection of the angle bisector at C.", "im_path": "/images_full/task_08196_bisector.png", "im_dots_path": "/images/task_08196_bisector_C.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex C meet the opposite side?", "image_answer": {"point": [3.0237763281123935, 20.0]}, "choices": null, "image_choices": null}
+{"qid": 8197, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-16, 5], "B": [-8, 20], "C": [16, 12]}, "answer": {"point": [-3.138939096715707, 7.813357072593439]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-16, 5), B=(-8, 20), C=(16, 12); find the intersection of the angle bisector at B.", "im_path": "/images_full/task_08197_bisector.png", "im_dots_path": "/images/task_08197_bisector_B.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex B meet the opposite side?", "image_answer": {"point": [-3.138939096715707, 7.813357072593439]}, "choices": null, "image_choices": null}
+{"qid": 8198, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-6, -4], "B": [-19, -18], "C": [-16, 13]}, "answer": {"point": [-17.52387872884553, -2.746746864737152]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, -4), B=(-19, -18), C=(-16, 13); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08198_bisector.png", "im_dots_path": "/images/task_08198_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-17.52387872884553, -2.746746864737152]}, "choices": null, "image_choices": null}
+{"qid": 8199, "type": "numeric", "category_id": 81, "category": "Remarkable lines of a triangle", "difficulty": 2, "schema_type": "point", "points": {"A": [-11, 8], "B": [-12, 11], "C": [-3, 12]}, "answer": {"point": [-9.649165125326327, 11.26120387496374]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-11, 8), B=(-12, 11), C=(-3, 12); find the intersection of the angle bisector at A.", "im_path": "/images_full/task_08199_bisector.png", "im_dots_path": "/images/task_08199_bisector_A.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. Where does the angle bisector at vertex A meet the opposite side?", "image_answer": {"point": [-9.649165125326327, 11.26120387496374]}, "choices": null, "image_choices": null}