pid string | question string | image string | decoded_image image | choices list | unit string | precision float64 | answer string | question_type string | answer_type string | metadata dict | query string |
|---|---|---|---|---|---|---|---|---|---|---|---|
482 | In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO, what is the degree measure of angle ABO? | images/482.jpg | [
"15*\\degree",
"30*\\degree",
"45*\\degree",
"60*\\degree",
"90*\\degree"
] | null | null | 60*\degree | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 134,
"img_width": 143,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO, what is the degree measure of angle ABO?
Choices:
(A) 15*\degree
(B) 30*\degree
(C) 45*\degree
(D) 60*\d... | |
483 | As shown in the figure, AB is the diameter of ⊙O, point C is on ⊙O, AE is the tangent of ⊙O, A is the tangent point, connect BC and extend to intersect AE at point D. If ∠AOC = 80.0, then the degree of ∠ADB is () | images/483.jpg | [
"40°",
"50°",
"60°",
"20°"
] | null | null | 50° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 129,
"img_width": 165,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, AB is the diameter of ⊙O, point C is on ⊙O, AE is the tangent of ⊙O, A is the tangent point, connect BC and extend to intersect AE at point D. If ∠AOC = 80.0, then the degree of ∠ADB i... | |
485 | 如图，点D在等边△ABC的边CB的延长线上，点E在线段BC上，连接AD，AE，若DA＝DE，且∠DAB＝20°，那么∠EAC的度数为（） | images/485.jpg | [
"20°",
"15°",
"10°",
"5°"
] | null | null | 10° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 110,
"img_width": 235,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，点D在等边△ABC的边CB的延长线上，点E在线段BC上，连接AD，AE，若DA＝DE，且∠DAB＝20°，那么∠EAC的度数为（）
Choices:
(A) 20°
(B) 15°
(C) 10°
(D) 5° | |
486 | 如图，在ABCD中，AB＝5，AD＝7，则ABCD的周长为（） | images/486.jpg | [
"12",
"14",
"35",
"24"
] | null | null | 24 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 79,
"img_width": 156,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在ABCD中，AB＝5，AD＝7，则ABCD的周长为（）
Choices:
(A) 12
(B) 14
(C) 35
(D) 24 | |
489 | For trapezoid ABCD shown above, AB = 24, AD = 23, and BC = 16. What is the length of segment CD? | images/489.jpg | null | null | null | 25 | free_form | integer | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 297,
"img_width": 426,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, 3, at the end.
Question: For trapezoid ABCD shown above, AB = 24, AD = 23, and BC = 16. What is the length of segment CD? | |
490 | 如图，点A、C、B在同一直线上，DC⊥EC，若∠BCD＝40°，则∠ACE的度数是（） | images/490.jpg | [
"30°",
"40°",
"50°",
"60°"
] | null | null | 50° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 88,
"img_width": 155,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，点A、C、B在同一直线上，DC⊥EC，若∠BCD＝40°，则∠ACE的度数是（）
Choices:
(A) 30°
(B) 40°
(C) 50°
(D) 60° | |
492 | As shown in the figure, in the ⊙O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that ∠DAC = 30.0, the length of the line segment CD is () | images/492.jpg | [
"1",
"√{3}",
"2",
"2√{3}"
] | null | null | 2√{3} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 158,
"img_width": 203,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in the ⊙O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that ∠DAC = 30.0, the length of the line... | |
499 | Quadrilateral $ABDC$ is a rectangle. If $m\angle1 = 38$, find $m \angle 2$ | images/499.jpg | [
"33",
"38",
"52",
"87"
] | null | null | 52 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 323,
"img_width": 559,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Quadrilateral $ABDC$ is a rectangle. If $m\angle1 = 38$, find $m \angle 2$
Choices:
(A) 33
(B) 38
(C) 52
(D) 87 | |
504 | As shown in the figure, D and E are the points on the edges AB and AC of △ABC, DE ∥ BC, if AD:DB=1.0:3.0, AE = 2.0, then the length of AC is () | images/504.jpg | [
"10",
"8",
"6",
"4"
] | null | null | 8 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 86,
"img_width": 117,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, D and E are the points on the edges AB and AC of △ABC, DE ∥ BC, if AD:DB=1.0:3.0, AE = 2.0, then the length of AC is ()
Choices:
(A) 10
(B) 8
(C) 6
(D) 4 | |
505 | As shown in the figure, in the circle O with a radius of 5.0, the length of the chord AB is 8.0, then the distance from the center O to the chord AB is () | images/505.jpg | [
"3",
"4",
"5",
"6"
] | null | null | 3 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 92,
"img_width": 100,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in the circle O with a radius of 5.0, the length of the chord AB is 8.0, then the distance from the center O to the chord AB is ()
Choices:
(A) 3
(B) 4
(C) 5
(D) 6 | |
510 | As shown in the figure, in Rt△ABC, ∠C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is () | images/510.jpg | [
"\\frac{2}{3}",
"\\frac{3}{5}",
"\\frac{3}{4}",
"\\frac{4}{5}"
] | null | null | \frac{4}{5} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 186,
"img_width": 119,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in Rt△ABC, ∠C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()
Choices:
(A) \frac{2}{3}
(B) \frac{3}{5}
(C) \frac{3}{4}
(D) \frac{4}{5} | |
521 | As shown in the figure, AB is the diameter of ⊙O, point C is a point on ⊙O, ∠C = 20.0, then the degree of ∠BOC is () | images/521.jpg | [
"20°",
"30°",
"40°",
"60°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 100,
"img_width": 120,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, AB is the diameter of ⊙O, point C is a point on ⊙O, ∠C = 20.0, then the degree of ∠BOC is ()
Choices:
(A) 20°
(B) 30°
(C) 40°
(D) 60° | |
523 | As shown in the figure, a teaching interest group wants to measure the height of a tree CD. They firstly measured the elevation angle of the tree top C at point A as 30.0, and then proceeded 10.0 along the direction of AD to point B, and the elevation angle of tree top C measured at B is 60.0 (the three points A, B, a... | images/523.jpg | [
"10m",
"5m",
"5√{3}m",
"10√{3}m"
] | null | null | 5√{3}m | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 179,
"img_width": 285,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, a teaching interest group wants to measure the height of a tree CD. They firstly measured the elevation angle of the tree top C at point A as 30.0, and then proceeded 10.0 along the di... | |
528 | 如图，AB∥CD，BD⊥CF，垂足为B，∠ABF＝35°，则∠BDC的度数为（） | images/528.jpg | [
"25°",
"35°",
"45°",
"55°"
] | null | null | 55° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 135,
"img_width": 194,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，AB∥CD，BD⊥CF，垂足为B，∠ABF＝35°，则∠BDC的度数为（）
Choices:
(A) 25°
(B) 35°
(C) 45°
(D) 55° | |
536 | As shown in the figure, points A, B, and C are on ⊙O, if ∠C = 35.0, then ∠AOB = () | images/536.jpg | [
"17.5°",
"35°",
"60°",
"70°"
] | null | null | 70° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 105,
"img_width": 115,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, points A, B, and C are on ⊙O, if ∠C = 35.0, then ∠AOB = ()
Choices:
(A) 17.5°
(B) 35°
(C) 60°
(D) 70° | |
538 | As shown in the figure, in the two concentric circles, the chord AB of the great circle is tangent to the small circle at point C. If AB = 6.0, the area of the ring is () | images/538.jpg | [
"9π",
"6π",
"3π",
"π"
] | null | null | 9π | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 111,
"img_width": 115,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in the two concentric circles, the chord AB of the great circle is tangent to the small circle at point C. If AB = 6.0, the area of the ring is ()
Choices:
(A) 9π
(B) 6π
(C) 3π
(D) π | |
539 | 如图，在△ABC中，点D、E分别是边AB、BC的中点，若△BDE的周长是6，则△ABC的周长是（） | images/539.jpg | [
"8",
"10",
"12",
"14"
] | null | null | 12 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 71,
"img_width": 149,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在△ABC中，点D、E分别是边AB、BC的中点，若△BDE的周长是6，则△ABC的周长是（）
Choices:
(A) 8
(B) 10
(C) 12
(D) 14 | |
549 | As shown in the figure, PA and PB are tangent to ⊙O to A and B respectively. Point C and point D are the moving points on line segments PA and PB, and CD always remains tangent to circle O. If PA = 8.0, then perimeter of △PCD is () | images/549.jpg | [
"8",
"12",
"16",
"不能确定"
] | null | null | 16 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 111,
"img_width": 192,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, PA and PB are tangent to ⊙O to A and B respectively. Point C and point D are the moving points on line segments PA and PB, and CD always remains tangent to circle O. If PA = 8.0, then ... | |
557 | 如图，在Rt△ABC中，∠BAC＝90°，以Rt△ABC的三边为边分别向外作等边三角形△A'BC，△AB'C，△ABC'，若△A'BC，△AB'C的面积分别是10和4，则△ABC'的面积是（） | images/557.jpg | [
"4",
"6",
"8",
"9"
] | null | null | 6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 130,
"img_width": 155,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在Rt△ABC中，∠BAC＝90°，以Rt△ABC的三边为边分别向外作等边三角形△A'BC，△AB'C，△ABC'，若△A'BC，△AB'C的面积分别是10和4，则△ABC'的面积是（）
Choices:
(A) 4
(B) 6
(C) 8
(D) 9 | |
566 | 如图，已知△ABC≌△DEF，CD平分∠BCA，若∠A＝22°，∠CGF＝88°，则∠E的度数是（） | images/566.jpg | [
"26°",
"28°",
"30°",
"34°"
] | null | null | 26° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 89,
"img_width": 89,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，已知△ABC≌△DEF，CD平分∠BCA，若∠A＝22°，∠CGF＝88°，则∠E的度数是（）
Choices:
(A) 26°
(B) 28°
(C) 30°
(D) 34° | |
575 | Lines $l$, $m$, and $n$ are perpendicular bisectors of $\triangle PQR$ and meet at $T$. If $TQ = 2x$, $PT = 3y - 1$, and $TR = 8$, find $z$. | images/575.jpg | [
"3",
"4",
"5",
"6"
] | null | null | 3 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 287,
"img_width": 509,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Lines $l$, $m$, and $n$ are perpendicular bisectors of $\triangle PQR$ and meet at $T$. If $TQ = 2x$, $PT = 3y - 1$, and $TR = 8$, find $z$.
Choices:
(A) 3
(B) 4
(C) 5
(D) 6 | |
583 | Find x. Round to the nearest tenth.
| images/583.jpg | [
"5.8",
"6.5",
"14.2",
"44.3"
] | null | null | 5.8 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 465,
"img_width": 319,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x. Round to the nearest tenth.
Choices:
(A) 5.8
(B) 6.5
(C) 14.2
(D) 44.3 | |
585 | 如图，在矩形ABCD中，AB＝2，∠AOB＝60°，则BD的长为（） | images/585.jpg | [
"4",
"3",
"2",
"2√{3}"
] | null | null | 4 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 92,
"img_width": 148,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在矩形ABCD中，AB＝2，∠AOB＝60°，则BD的长为（）
Choices:
(A) 4
(B) 3
(C) 2
(D) 2√{3} | |
586 | As shown in the figure, in Rt△ABC, ∠BAC = 90.0, rotate △ABC clockwise around point A by 90.0 to obtain △AB′C′ (the corresponding point of point B is point B′, and the corresponding point of point C is point C ′), connect CC′. If ∠CC′B′ = 32.0, then the size of ∠AC′B′ is () | images/586.jpg | [
"32°",
"45°",
"13°",
"30°"
] | null | null | 13° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 75,
"img_width": 80,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in Rt△ABC, ∠BAC = 90.0, rotate △ABC clockwise around point A by 90.0 to obtain △AB′C′ (the corresponding point of point B is point B′, and the corresponding point of point C is point C... | |
587 | At 9.0 in the morning, a ship departs from point A and sails in the direction due east at a speed of 40.0 nautical miles per hour, and arrives at point B at 9.0 and 30.0 minutes. As shown in the figure, the island M is measured from A and B. In the direction of 45.0 north by east and 15.0 north by east, then the distan... | images/587.jpg | [
"20海里",
"20√{2}海里",
"15海里",
"20海里"
] | null | null | 20√{2}海里 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 124,
"img_width": 144,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: At 9.0 in the morning, a ship departs from point A and sails in the direction due east at a speed of 40.0 nautical miles per hour, and arrives at point B at 9.0 and 30.0 minutes. As shown in the figure, the i... | |
599 | In the figure above, AC = 6 and BC = 3. Point P lies on line AB between A and B such that line CP is perpendicular to line AB. Which of the following could be the length of line CP? | images/599.jpg | [
"2",
"4",
"5",
"7",
"8"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 340,
"img_width": 393,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, AC = 6 and BC = 3. Point P lies on line AB between A and B such that line CP is perpendicular to line AB. Which of the following could be the length of line CP?
Choices:
(A) 2
(B) 4
(C) 5... | |
602 | Rectangle ABCD is subdivided into two identical square regions, as in the figure above. If the area of each square is 9, what is the perimeter of ABCD? | images/602.jpg | null | null | null | 18 | free_form | integer | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 219,
"img_width": 435,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, 3, at the end.
Question: Rectangle ABCD is subdivided into two identical square regions, as in the figure above. If the area of each square is 9, what is the perimeter of ABCD? | |
610 | In the figure above, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4, what is the radius of the smaller circle? | images/610.jpg | [
"1",
"2",
"4",
"8",
"16"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 353,
"img_width": 411,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4, what is the radius of the small... | |
615 | If two sides of a triangle measure 12 and 7, which of the following cannot be the perimeter of the triangle? | images/615.jpg | [
"29",
"34",
"37",
"38"
] | null | null | 38 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 195,
"img_width": 522,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: If two sides of a triangle measure 12 and 7, which of the following cannot be the perimeter of the triangle?
Choices:
(A) 29
(B) 34
(C) 37
(D) 38 | |
621 | The figure above is composed of 25 small triangles that are congruent and equilateral. If the area of triangle DFH is 10, what is the area of triangle AFK? | images/621.jpg | [
"40",
"42.5",
"50",
"52.5",
"62.5"
] | null | null | 62.5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 315,
"img_width": 397,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: The figure above is composed of 25 small triangles that are congruent and equilateral. If the area of triangle DFH is 10, what is the area of triangle AFK?
Choices:
(A) 40
(B) 42.5
(C) 50
(D) 52.5
(E) 62.5 | |
622 | 如图，在△ABC中，D是BC上的点，且BD＝2，DC＝1，S△ACD＝12，那么S△ABC等于（） | images/622.jpg | [
"30",
"36",
"72",
"24"
] | null | null | 36 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 92,
"img_width": 146,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在△ABC中，D是BC上的点，且BD＝2，DC＝1，S△ACD＝12，那么S△ABC等于（）
Choices:
(A) 30
(B) 36
(C) 72
(D) 24 | |
628 | 如图，在ABCD中，∠ABC的平分线交AD于点E，∠BCD的平分线交AD于点F，若AB＝3，AD＝4，则EF的长是（） | images/628.jpg | [
"1",
"2",
"2.5",
"3"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 111,
"img_width": 151,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在ABCD中，∠ABC的平分线交AD于点E，∠BCD的平分线交AD于点F，若AB＝3，AD＝4，则EF的长是（）
Choices:
(A) 1
(B) 2
(C) 2.5
(D) 3 | |
633 | In the figure, $m∠1 = 123$. Find the measure of $\angle 14$. | images/633.jpg | [
"47",
"57",
"67",
"123"
] | null | null | 57 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 330,
"img_width": 361,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure, $m∠1 = 123$. Find the measure of $\angle 14$.
Choices:
(A) 47
(B) 57
(C) 67
(D) 123 | |
634 | 如图，直线AB，CD交于点O．射线OE平分∠BOC，若∠AOD＝70°，则∠AOE等于（） | images/634.jpg | [
"35°",
"110°",
"135°",
"145°"
] | null | null | 145° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 141,
"img_width": 173,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，直线AB，CD交于点O．射线OE平分∠BOC，若∠AOD＝70°，则∠AOE等于（）
Choices:
(A) 35°
(B) 110°
(C) 135°
(D) 145° | |
635 | As shown in the figure, E is any point in ▱ABCD, if S~quadrilateral ABCD~ = 6.0, then the area of the shaded part in the figure is () | images/635.jpg | [
"2",
"3",
"4",
"5"
] | null | null | 3 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 86,
"img_width": 179,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, E is any point in ▱ABCD, if S~quadrilateral ABCD~ = 6.0, then the area of the shaded part in the figure is ()
Choices:
(A) 2
(B) 3
(C) 4
(D) 5 | |
637 | 如图，直线a∥b，直线a与矩形ABCD的边AB，AD分别交于点E，F，直线b与矩形ABCD的边CB，CD分别交于点G，H．若∠AFE＝30°，则∠DHG的度数为（） | images/637.jpg | [
"100°",
"110°",
"120°",
"130°"
] | null | null | 120° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 108,
"img_width": 166,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，直线a∥b，直线a与矩形ABCD的边AB，AD分别交于点E，F，直线b与矩形ABCD的边CB，CD分别交于点G，H．若∠AFE＝30°，则∠DHG的度数为（）
Choices:
(A) 100°
(B) 110°
(C) 120°
(D) 130° | |
640 | Find $\widehat{\mathrm{WN}}$ if $\triangle \mathrm{IWN}$ is equilateral and $W N=5$ | images/640.jpg | [
"\\frac { 3 } { 5 } \\pi",
"\\frac { 5 } { 3 } \\pi",
"5 \\pi",
"10 \\pi"
] | null | null | \frac { 5 } { 3 } \pi | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 222,
"img_width": 309,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $\widehat{\mathrm{WN}}$ if $\triangle \mathrm{IWN}$ is equilateral and $W N=5$
Choices:
(A) \frac { 3 } { 5 } \pi
(B) \frac { 5 } { 3 } \pi
(C) 5 \pi
(D) 10 \pi | |
642 | Line AB is tangent to circle O. If AB = 8 and OB = 10, find the diameter of the circle. | images/642.jpg | [
"4",
"6",
"8",
"10",
"12"
] | null | null | 12 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 443,
"img_width": 347,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Line AB is tangent to circle O. If AB = 8 and OB = 10, find the diameter of the circle.
Choices:
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12 | |
643 | As shown in the figure, CD is the diameter of ⊙O, chord DE ∥ OA, if the degree of ∠D is 50.0, then the degree of ∠C is () | images/643.jpg | [
"25°",
"30°",
"40°",
"50°"
] | null | null | 25° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 125,
"img_width": 111,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, CD is the diameter of ⊙O, chord DE ∥ OA, if the degree of ∠D is 50.0, then the degree of ∠C is ()
Choices:
(A) 25°
(B) 30°
(C) 40°
(D) 50° | |
645 | 如图，AC，BD是菱形ABCD的对角线，BH⊥AD于点H，若AC＝4，BD＝3，则BH的长为（） | images/645.jpg | [
"2.4",
"2.5",
"4.8",
"5"
] | null | null | 2.4 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 113,
"img_width": 139,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，AC，BD是菱形ABCD的对角线，BH⊥AD于点H，若AC＝4，BD＝3，则BH的长为（）
Choices:
(A) 2.4
(B) 2.5
(C) 4.8
(D) 5 | |
665 | Find $h$ in the triangle. | images/665.jpg | [
"4.62",
"5.66",
"6.93",
"8"
] | null | null | 8 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 161,
"img_width": 275,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $h$ in the triangle.
Choices:
(A) 4.62
(B) 5.66
(C) 6.93
(D) 8 | |
669 | As shown in the figure, line segment AB = 10.0, M is the midpoint of line segment AB, C is the midpoint of line segment MB, N is a point of line segment AM, and MN = 1.0, the length of line segment NC () | images/669.jpg | [
"2",
"2.5",
"3",
"3.5"
] | null | null | 3.5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 18,
"img_width": 187,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, line segment AB = 10.0, M is the midpoint of line segment AB, C is the midpoint of line segment MB, N is a point of line segment AM, and MN = 1.0, the length of line segment NC ()
Choi... | |
674 | In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE? | images/674.jpg | [
"4",
"5",
"6",
"7",
"8"
] | null | null | 5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 89,
"img_width": 125,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE?
Choices:
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8 | |
675 | As shown in the figure, the cross section of a small reservoir dam is a right trapezoid, the width of crest BC is 6.0, the height of dam is 14.0, and the slope of the slope CD is i = 1.0:2.0, then the length of the dam bottom AD is () | images/675.jpg | [
"13m",
"34m",
"(6+14√{3})m",
"40m"
] | null | null | 34m | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 83,
"img_width": 183,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, the cross section of a small reservoir dam is a right trapezoid, the width of crest BC is 6.0, the height of dam is 14.0, and the slope of the slope CD is i = 1.0:2.0, then the length ... | |
678 | Find x | images/678.jpg | [
"21",
"34",
"58",
"67"
] | null | null | 58 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 149,
"img_width": 267,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x
Choices:
(A) 21
(B) 34
(C) 58
(D) 67 | |
679 | As shown in the figure, in ▱ABCD, the diagonal AC and BD intersect at point O, if AC = 12.0, BD = 8.0, AB = 7.0, then the perimeter of △OAB is () | images/679.jpg | [
"15",
"17",
"21",
"27"
] | null | null | 17 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 73,
"img_width": 173,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in ▱ABCD, the diagonal AC and BD intersect at point O, if AC = 12.0, BD = 8.0, AB = 7.0, then the perimeter of △OAB is ()
Choices:
(A) 15
(B) 17
(C) 21
(D) 27 | |
684 | $\overline{CH} \cong \overline{KJ}$. Find $x$. | images/684.jpg | [
"27",
"54",
"55",
"83"
] | null | null | 55 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 444,
"img_width": 608,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: $\overline{CH} \cong \overline{KJ}$. Find $x$.
Choices:
(A) 27
(B) 54
(C) 55
(D) 83 | |
690 | In the diagram above, lines M and N are parallel. All of the following are true except | images/690.jpg | [
"a + b = j + l",
"g = h",
"c + f = f + b",
"g + e + f + h = 360",
"d + e = f + j"
] | null | null | d + e = f + j | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 558,
"img_width": 625,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the diagram above, lines M and N are parallel. All of the following are true except
Choices:
(A) a + b = j + l
(B) g = h
(C) c + f = f + b
(D) g + e + f + h = 360
(E) d + e = f + j | |
694 | 如图，在菱形ABCD中，M、N分别是BC和CD的中点，NP⊥AB于点P，连接MP．若∠DAB＝40°，则∠MPB＝（） | images/694.jpg | [
"125°",
"120°",
"115°",
"110°"
] | null | null | 110° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 85,
"img_width": 158,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在菱形ABCD中，M、N分别是BC和CD的中点，NP⊥AB于点P，连接MP．若∠DAB＝40°，则∠MPB＝（）
Choices:
(A) 125°
(B) 120°
(C) 115°
(D) 110° | |
697 | As shown in the figure, in the parallelogram ABCD, it is known that AB = 6.0, BC = 9.0, ∠B = 30.0, then the area of the parallelogram ABCD is () | images/697.jpg | [
"12",
"18",
"27",
"54"
] | null | null | 27 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 68,
"img_width": 205,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in the parallelogram ABCD, it is known that AB = 6.0, BC = 9.0, ∠B = 30.0, then the area of the parallelogram ABCD is ()
Choices:
(A) 12
(B) 18
(C) 27
(D) 54 | |
698 | In the triangle in the figure above, what is the value of x? | images/698.jpg | [
"2*\\sqrt{3}",
"6*\\sqrt{2}",
"6*\\sqrt{3}",
"6",
"12"
] | null | null | 2*\sqrt{3} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 376,
"img_width": 615,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the triangle in the figure above, what is the value of x?
Choices:
(A) 2*\sqrt{3}
(B) 6*\sqrt{2}
(C) 6*\sqrt{3}
(D) 6
(E) 12 | |
700 | 如图，⊙O是△ABC的外接圆，AB＝BC＝4，把弧AB沿弦AB向下折叠交BC于点D，若点D为BC中点，则AC长为（） | images/700.jpg | [
"1",
"2",
"2√{2}",
"√{6}"
] | null | null | 2√{2} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 132,
"img_width": 144,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，⊙O是△ABC的外接圆，AB＝BC＝4，把弧AB沿弦AB向下折叠交BC于点D，若点D为BC中点，则AC长为（）
Choices:
(A) 1
(B) 2
(C) 2√{2}
(D) √{6} | |
707 | 如图，a∥b，∠1＝60°，则∠2的大小是（） | images/707.jpg | [
"60°",
"80°",
"100°",
"120°"
] | null | null | 120° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 120,
"img_width": 154,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，a∥b，∠1＝60°，则∠2的大小是（）
Choices:
(A) 60°
(B) 80°
(C) 100°
(D) 120° | |
708 | As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB ∥ CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is (). | images/708.jpg | [
"\\frac{6}{5}",
"\\frac{7}{6}",
"\\frac{9}{5}",
"\\frac{15}{2}"
] | null | null | \frac{9}{5} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 110,
"img_width": 156,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB ∥ CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance... | |
713 | Find $x$. | images/713.jpg | [
"3",
"4",
"6",
"7"
] | null | null | 3 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 422,
"img_width": 521,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $x$.
Choices:
(A) 3
(B) 4
(C) 6
(D) 7 | |
716 | Find y. | images/716.jpg | [
"16 \\sqrt { 2 }",
"16 \\sqrt { 3 }",
"32",
"16 \\sqrt { 5 }"
] | null | null | 16 \sqrt { 5 } | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 196,
"img_width": 427,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find y.
Choices:
(A) 16 \sqrt { 2 }
(B) 16 \sqrt { 3 }
(C) 32
(D) 16 \sqrt { 5 } | |
726 | Find x. Assume that any segment that appears to be tangent is tangent. | images/726.jpg | [
"10",
"30",
"90",
"120"
] | null | null | 10 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 199,
"img_width": 228,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x. Assume that any segment that appears to be tangent is tangent.
Choices:
(A) 10
(B) 30
(C) 90
(D) 120 | |
736 | 如图，已知直线a∥b，直角三角形ABC中，∠C＝90°，若∠B＝58°，那么∠1﹣∠2＝（） | images/736.jpg | [
"28°",
"30°",
"32°",
"58°"
] | null | null | 32° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 154,
"img_width": 226,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，已知直线a∥b，直角三角形ABC中，∠C＝90°，若∠B＝58°，那么∠1﹣∠2＝（）
Choices:
(A) 28°
(B) 30°
(C) 32°
(D) 58° | |
737 | Find the perimeter of the parallelogram. | images/737.jpg | [
"32",
"39",
"46",
"78"
] | null | null | 78 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 179,
"img_width": 352,
"language": "english",
"skills": [
"geometry reasoning",
"arithmetic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
... | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find the perimeter of the parallelogram.
Choices:
(A) 32
(B) 39
(C) 46
(D) 78 | |
744 | If RL = 5, RT = 9, and WS = 6, find RW. | images/744.jpg | [
"5.4",
"6",
"6.6",
"7.5"
] | null | null | 7.5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 199,
"img_width": 404,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: If RL = 5, RT = 9, and WS = 6, find RW.
Choices:
(A) 5.4
(B) 6
(C) 6.6
(D) 7.5 | |
747 | In $\odot M$, $FL=24,HJ=48$, and $m \widehat {HP}=65$. Find $m \widehat {HJ}$. | images/747.jpg | [
"65",
"120",
"130",
"155"
] | null | null | 130 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 467,
"img_width": 507,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In $\odot M$, $FL=24,HJ=48$, and $m \widehat {HP}=65$. Find $m \widehat {HJ}$.
Choices:
(A) 65
(B) 120
(C) 130
(D) 155 | |
748 | As shown in the figure, PA and PB are tangents of ⊙O, the tangent point of point A and B, AC is the diameter of ⊙O, given that ∠P = 50.0, then the size of ∠ACB is () | images/748.jpg | [
"65°",
"60°",
"55°",
"50°"
] | null | null | 65° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 117,
"img_width": 207,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, PA and PB are tangents of ⊙O, the tangent point of point A and B, AC is the diameter of ⊙O, given that ∠P = 50.0, then the size of ∠ACB is ()
Choices:
(A) 65°
(B) 60°
(C) 55°
(D) 50° | |
749 | As shown in the figure, in △ABC, DE ∥ BC, if AB = 7.0, AC = 5.0, AD = 3.0, then DE = () | images/749.jpg | [
"\\frac{15}{4}cm",
"\\frac{20}{3}cm",
"\\frac{15}{7}cm",
"\\frac{20}{7}cm"
] | null | null | \frac{20}{7}cm | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 98,
"img_width": 181,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in △ABC, DE ∥ BC, if AB = 7.0, AC = 5.0, AD = 3.0, then DE = ()
Choices:
(A) \frac{15}{4}cm
(B) \frac{20}{3}cm
(C) \frac{15}{7}cm
(D) \frac{20}{7}cm | |
752 | 如图，PA是⊙O的切线，切点为A，OP＝4，∠APO＝30°，则⊙O的半径长为（） | images/752.jpg | [
"1",
"√{3}",
"2",
"3"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 87,
"img_width": 122,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，PA是⊙O的切线，切点为A，OP＝4，∠APO＝30°，则⊙O的半径长为（）
Choices:
(A) 1
(B) √{3}
(C) 2
(D) 3 | |
757 | Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent. | images/757.jpg | [
"7.2",
"8",
"12",
"15"
] | null | null | 7.2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 165,
"img_width": 220,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.
Choices:
(A) 7.2
(B) 8
(C) 12
(D) 15 | |
773 | As shown in the figure, AB is the diameter of ⊙O, point D is on the extended line of AB, passing point D is the tangent of ⊙O, and the tangent point is C, if ∠A = 25.0, then ∠D = () | images/773.jpg | [
"25°",
"40°",
"50°",
"65°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 117,
"img_width": 163,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, AB is the diameter of ⊙O, point D is on the extended line of AB, passing point D is the tangent of ⊙O, and the tangent point is C, if ∠A = 25.0, then ∠D = ()
Choices:
(A) 25°
(B) 40°
(... | |
776 | Find $JQ$ if $Q$ is the incenter of $\triangle JLN$. Rounded to the nearest hundredth. | images/776.jpg | [
"16.50",
"18.79",
"20.32",
"25.50"
] | null | null | 18.79 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 424,
"img_width": 589,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $JQ$ if $Q$ is the incenter of $\triangle JLN$. Rounded to the nearest hundredth.
Choices:
(A) 16.50
(B) 18.79
(C) 20.32
(D) 25.50 | |
777 | In rhombus LMPQ, $m \angle Q L M=2 x^{2}-10$, $m \angle Q P M=8 x$, and $M P=10$ .
Find the perimeter of $LMPQ$ | images/777.jpg | [
"10",
"40",
"70",
"140"
] | null | null | 40 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 177,
"img_width": 337,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In rhombus LMPQ, $m \angle Q L M=2 x^{2}-10$, $m \angle Q P M=8 x$, and $M P=10$ .
Find the perimeter of $LMPQ$
Choices:
(A) 10
(B) 40
(C) 70
(D) 140 | |
781 | In $\triangle CDF$, $K$ is the centroid and $DK=16$. Find $CD$. | images/781.jpg | [
"9",
"12",
"18",
"18"
] | null | null | 18 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 540,
"img_width": 461,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In $\triangle CDF$, $K$ is the centroid and $DK=16$. Find $CD$.
Choices:
(A) 9
(B) 12
(C) 18
(D) 18 | |
783 | In order to measure the width of parallel river AB, ∠ACB = 30.0, ∠ADB = 60.0, CD = 60.0, then the width of the river AB is () | images/783.jpg | [
"30m",
"30√{3}m",
"(30√{3}+30)m",
"(30√{3}-30)m"
] | null | null | 30√{3}m | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 87,
"img_width": 130,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In order to measure the width of parallel river AB, ∠ACB = 30.0, ∠ADB = 60.0, CD = 60.0, then the width of the river AB is ()
Choices:
(A) 30m
(B) 30√{3}m
(C) (30√{3}+30)m
(D) (30√{3}-30)m | |
786 | Find $m \angle K$ | images/786.jpg | [
"6",
"60",
"100",
"180"
] | null | null | 100 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 237,
"img_width": 317,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $m \angle K$
Choices:
(A) 6
(B) 60
(C) 100
(D) 180 | |
790 | 如图，△ABC中，N是BC边上的中点，AM平分∠BAC，BM⊥AM于点M，若AB＝8，MN＝2．则AC的长为（） | images/790.jpg | [
"10",
"11",
"12",
"13"
] | null | null | 12 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 105,
"img_width": 145,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，△ABC中，N是BC边上的中点，AM平分∠BAC，BM⊥AM于点M，若AB＝8，MN＝2．则AC的长为（）
Choices:
(A) 10
(B) 11
(C) 12
(D) 13 | |
798 | In the figure above, l || m. Which of the following must equal 180? | images/798.jpg | [
"k + n + r",
"k + p + s",
"n + p + s",
"n + p + t",
"r + s + t"
] | null | null | k + p + s | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 372,
"img_width": 371,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, l || m. Which of the following must equal 180?
Choices:
(A) k + n + r
(B) k + p + s
(C) n + p + s
(D) n + p + t
(E) r + s + t | |
804 | In $\odot B$, $CE=13.5$. Find $BD$. Round to the nearest hundredth. | images/804.jpg | [
"3.71",
"4.29",
"4.53",
"6.75"
] | null | null | 4.29 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 524,
"img_width": 493,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In $\odot B$, $CE=13.5$. Find $BD$. Round to the nearest hundredth.
Choices:
(A) 3.71
(B) 4.29
(C) 4.53
(D) 6.75 | |
806 | As shown in the figure, AB is the diameter of ⊙O, and point C is on ⊙O. If ∠A = 40.0, then the degree of ∠B is () | images/806.jpg | [
"80°",
"60°",
"50°",
"40°"
] | null | null | 50° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 107,
"img_width": 127,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, AB is the diameter of ⊙O, and point C is on ⊙O. If ∠A = 40.0, then the degree of ∠B is ()
Choices:
(A) 80°
(B) 60°
(C) 50°
(D) 40° | |
815 | Find $m \angle N C L$ | images/815.jpg | [
"60",
"120",
"240",
"360"
] | null | null | 120 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 279,
"img_width": 367,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $m \angle N C L$
Choices:
(A) 60
(B) 120
(C) 240
(D) 360 | |
816 | Find x. Round to the nearest tenth, if necessary. | images/816.jpg | [
"3",
"9",
"12.25",
"24"
] | null | null | 3 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 272,
"img_width": 379,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x. Round to the nearest tenth, if necessary.
Choices:
(A) 3
(B) 9
(C) 12.25
(D) 24 | |
817 | As shown in the figure, the straight line a ∥ b, the point B is on the straight line b, and AB ⊥ BC, ∠2 = 65.0, then the degree of ∠1 is () | images/817.jpg | [
"65°",
"25°",
"35°",
"45°"
] | null | null | 25° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 94,
"img_width": 171,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, the straight line a ∥ b, the point B is on the straight line b, and AB ⊥ BC, ∠2 = 65.0, then the degree of ∠1 is ()
Choices:
(A) 65°
(B) 25°
(C) 35°
(D) 45° | |
819 | Find the value of $t$ in the parallelogram. | images/819.jpg | [
"6",
"7",
"8",
"13"
] | null | null | 7 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 400,
"img_width": 428,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find the value of $t$ in the parallelogram.
Choices:
(A) 6
(B) 7
(C) 8
(D) 13 | |
820 | $a=14, b=48,$ and $c=50$ find $cosA$ | images/820.jpg | [
"0.14",
"0.48",
"0.50",
"0.96"
] | null | null | 0.96 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 160,
"img_width": 238,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: $a=14, b=48,$ and $c=50$ find $cosA$
Choices:
(A) 0.14
(B) 0.48
(C) 0.50
(D) 0.96 | |
822 | Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | images/822.jpg | [
"22",
"40",
"44",
"48"
] | null | null | 44 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 227,
"img_width": 356,
"language": "english",
"skills": [
"geometry reasoning",
"arithmetic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
... | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.
Choices:
(A) 22
(B) 40
(C) 44
(D) 48 | |
842 | At a certain moment, there is a passenger ship at sea point P, and lighthouse A is measured in the direction 30.0 north by east of P, and is 50.0 nautical miles away. The passenger ship sails at the speed of 60.0 nautical mile/hour in the direction of 60.0 from north by west for $\frac{2.0}{3.0}$hours to reach point B,... | images/842.jpg | [
"\\frac{4}{5}",
"\\frac{6}{5}",
"\\frac{√{5}}{5}",
"\\frac{2√{5}}{5}"
] | null | null | \frac{4}{5} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 115,
"img_width": 154,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: At a certain moment, there is a passenger ship at sea point P, and lighthouse A is measured in the direction 30.0 north by east of P, and is 50.0 nautical miles away. The passenger ship sails at the speed of ... | |
853 | As shown in the figure, in the diamond ABCD, ∠BAD = 120.0, the length of the diagonal AC is 3.0, then the perimeter of the diamond ABCD is () | images/853.jpg | [
"3",
"6",
"9",
"12"
] | null | null | 12 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 98,
"img_width": 169,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in the diamond ABCD, ∠BAD = 120.0, the length of the diagonal AC is 3.0, then the perimeter of the diamond ABCD is ()
Choices:
(A) 3
(B) 6
(C) 9
(D) 12 | |
855 | Find $x$ so that $a ∥ b$. | images/855.jpg | [
"2.5",
"14",
"15",
"16"
] | null | null | 14 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 250,
"img_width": 536,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $x$ so that $a ∥ b$.
Choices:
(A) 2.5
(B) 14
(C) 15
(D) 16 | |
866 | For trapezoid $Q R S T, A$ and $B$ are midpoints of the legs. Find $m \angle S$ | images/866.jpg | [
"45",
"60",
"120",
"135"
] | null | null | 135 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 169,
"img_width": 359,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: For trapezoid $Q R S T, A$ and $B$ are midpoints of the legs. Find $m \angle S$
Choices:
(A) 45
(B) 60
(C) 120
(D) 135 | |
876 | In the figure, square $ABDC$ is inscribed in $\odot K$. Find the measure of a central angle. | images/876.jpg | [
"45",
"60",
"90",
"180"
] | null | null | 90 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 275,
"img_width": 273,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure, square $ABDC$ is inscribed in $\odot K$. Find the measure of a central angle.
Choices:
(A) 45
(B) 60
(C) 90
(D) 180 | |
878 | 如图，在Rt△ABC中，∠ACB＝90°，以Rt△ABC的三边为边向外作正方形，其面积分别为S1，S2，S3，且S1＝5，S3＝16，则S2＝（） | images/878.jpg | [
"6",
"2√{2}",
"11",
"24"
] | null | null | 11 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 82,
"img_width": 94,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在Rt△ABC中，∠ACB＝90°，以Rt△ABC的三边为边向外作正方形，其面积分别为S1，S2，S3，且S1＝5，S3＝16，则S2＝（）
Choices:
(A) 6
(B) 2√{2}
(C) 11
(D) 24 | |
887 | As shown in the figure, △ABC is the inscribed triangle of ⊙O. If ∠ABC = 70.0, then the degree of ∠AOC is equal to () | images/887.jpg | [
"140°",
"130°",
"120°",
"110°"
] | null | null | 140° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 106,
"img_width": 119,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, △ABC is the inscribed triangle of ⊙O. If ∠ABC = 70.0, then the degree of ∠AOC is equal to ()
Choices:
(A) 140°
(B) 130°
(C) 120°
(D) 110° | |
897 | Use a calculator to find the measure of $∠J$ to the nearest degree. | images/897.jpg | [
"33",
"40",
"50",
"57"
] | null | null | 40 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 223,
"img_width": 352,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Use a calculator to find the measure of $∠J$ to the nearest degree.
Choices:
(A) 33
(B) 40
(C) 50
(D) 57 | |
898 | As shown in the figure, A, B, and C are the three points on ⊙O, if ∠C = 35.0, then the degree of ∠OAB is () | images/898.jpg | [
"35°",
"55°",
"65°",
"70°"
] | null | null | 55° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 109,
"img_width": 112,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, A, B, and C are the three points on ⊙O, if ∠C = 35.0, then the degree of ∠OAB is ()
Choices:
(A) 35°
(B) 55°
(C) 65°
(D) 70° | |
903 | As shown in the figure, if ∠ABC = 30.0, then the degree of ∠AOC is () | images/903.jpg | [
"30°",
"45°",
"60°",
"70°"
] | null | null | 60° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 112,
"img_width": 110,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, if ∠ABC = 30.0, then the degree of ∠AOC is ()
Choices:
(A) 30°
(B) 45°
(C) 60°
(D) 70° | |
909 | As shown in the figure, in △ABC, DE ∥ BC, if AD = 1.0, DB = 2.0, then the value of \frac ADAB is () | images/909.jpg | [
"\\frac{2}{3}",
"\\frac{1}{4}",
"\\frac{1}{3}",
"\\frac{1}{2}"
] | null | null | \frac{1}{3} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 118,
"img_width": 132,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in △ABC, DE ∥ BC, if AD = 1.0, DB = 2.0, then the value of \frac ADAB is ()
Choices:
(A) \frac{2}{3}
(B) \frac{1}{4}
(C) \frac{1}{3}
(D) \frac{1}{2} | |
916 | As shown in the figure, in Rt△ABC, ∠C = 90.0, ∠A = 30.0, BC = 2.0, the radius of ⊙C is 1.0, point P is the point on the hypotenuse AB, passing point P is a tangent PQ of ⊙C (Point Q is the tangent point), then the minimum value of the line segment PQ is () | images/916.jpg | [
"2",
"√{3}",
"√{2}",
"2-\\frac{√{3}}{3}"
] | null | null | √{2} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 145,
"img_width": 112,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in Rt△ABC, ∠C = 90.0, ∠A = 30.0, BC = 2.0, the radius of ⊙C is 1.0, point P is the point on the hypotenuse AB, passing point P is a tangent PQ of ⊙C (Point Q is the tangent point), the... | |
920 | The measure of angle BAC equals x*\degree. What is the value of x? | images/920.jpg | null | null | null | 30 | free_form | integer | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 310,
"img_width": 388,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, 3, at the end.
Question: The measure of angle BAC equals x*\degree. What is the value of x? | |
921 | Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent. | images/921.jpg | [
"5",
"8.1",
"10.3",
"21.6"
] | null | null | 21.6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 170,
"img_width": 226,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.
Choices:
(A) 5
(B) 8.1
(C) 10.3
(D) 21.6 | |
927 | 如图，在△ABC中，AB的垂直平分线交AB于点D，交BC于点E，连接AE．若AB＝6，△ACE的周长为13，则△ABC的周长为（） | images/927.jpg | [
"19",
"16",
"29",
"18"
] | null | null | 19 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 152,
"img_width": 199,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在△ABC中，AB的垂直平分线交AB于点D，交BC于点E，连接AE．若AB＝6，△ACE的周长为13，则△ABC的周长为（）
Choices:
(A) 19
(B) 16
(C) 29
(D) 18 | |
930 | 如图，F是△ABC的角平分线CD和BE的交点，CG⊥AB于点G．若∠ACG＝32°，则∠BFC的度数是（） | images/930.jpg | [
"119°",
"122°",
"148°",
"150°"
] | null | null | 119° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 79,
"img_width": 113,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，F是△ABC的角平分线CD和BE的交点，CG⊥AB于点G．若∠ACG＝32°，则∠BFC的度数是（）
Choices:
(A) 119°
(B) 122°
(C) 148°
(D) 150° | |
931 | As shown in the figure, △ABC is the inscribed triangle of ⊙O, AB is the diameter of ⊙O, point D is a point on ⊙O, if ∠ACD = 40.0, then the size of ∠BAD is () | images/931.jpg | [
"35°",
"50°",
"40°",
"60°"
] | null | null | 50° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 123,
"img_width": 124,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, △ABC is the inscribed triangle of ⊙O, AB is the diameter of ⊙O, point D is a point on ⊙O, if ∠ACD = 40.0, then the size of ∠BAD is ()
Choices:
(A) 35°
(B) 50°
(C) 40°
(D) 60° | |
935 | 如图，在ABCD中，AD＝6，AB＝4，DE平分∠ADC交BC于点E，则BE的长是（） | images/935.jpg | [
"2",
"3",
"4",
"5"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 81,
"img_width": 140,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在ABCD中，AD＝6，AB＝4，DE平分∠ADC交BC于点E，则BE的长是（）
Choices:
(A) 2
(B) 3
(C) 4
(D) 5 | |
938 | In the figure, $m ∠9 = 75$. Find the measure of $\angle 6$. | images/938.jpg | [
"75",
"85",
"95",
"105"
] | null | null | 105 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 278,
"img_width": 417,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure, $m ∠9 = 75$. Find the measure of $\angle 6$.
Choices:
(A) 75
(B) 85
(C) 95
(D) 105 |
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