problem stringlengths 7 240 | answer stringlengths 1 34 | description stringlengths 0 1.63k | prompt stringlengths 969 2.58k | responses listlengths 32 32 | extracted_answers listlengths 32 32 | rewards listlengths 32 32 | mean_reward float64 0 1 |
|---|---|---|---|---|---|---|---|
If \overrightarrow A C bisects \angle D A B, B C = 4 x + 8, and D C = 9 x - 7, find B C. | 20 | "PointLiesOnLine(B, Line(E, F));PointLiesOnLine(D, Line(E, N));PointLiesOnLine(C, Line(E, A));Perpen(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a detailed textual description of a geometric configuration and a question involving (...TRUNCATED) | ["\\boxed{We are given a detailed textual description of a geometric configuration and a question in(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0 |
If m \widehat A E = 75, find m \angle A D E. | 37.5 | "PointLiesOnLine(N, Line(D, A));PointLiesOnCircle(D, Circle(N, radius_0_0));PointLiesOnCircle(A, Cir(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a detailed textual description of a geometric configuration and asked to find the mea(...TRUNCATED) | ["\\boxed{We are given a detailed textual description of a geometric configuration and asked to find(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0(...TRUNCATED) | 0.125 |
Find the value of x. Round to the nearest tenth. | 7.8 | "Equals(MeasureOf(Angle(C, A, F)), 70);Equals(LengthOf(Line(A, E)), x);Equals(MeasureOf(Angle(A, E, (...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a geometric configuration described textually. Let's interpret and analyze the inform(...TRUNCATED) | ["\\boxed{We are given a geometric configuration described textually. Let's interpret and analyze th(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0 |
Find y. Round to the nearest tenth. | 33.4 | "Equals(MeasureOf(Angle(C, B, D)), x);Equals(LengthOf(Line(A, B)), 40);Equals(LengthOf(Line(B, C)), (...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a detailed geometric description involving points A, B, C, D and various lengths, ang(...TRUNCATED) | ["\\boxed{We are given a detailed geometric description involving points A, B, C, D and various leng(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0 |
"In \\triangle P Q R, Z Q = 3 a - 11, Z P = a + 5, P Y = 2 c - 1, Y R = 4 c - 11, m \\angle P R Z = (...TRUNCATED) | 12 | "PointLiesOnLine(A, Line(X, Y));PointLiesOnLine(Y, Line(R, P));PointLiesOnLine(A, Line(R, Z));PointL(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a complex geometric configuration involving points, lines, and various lengths and an(...TRUNCATED) | ["\\boxed{We are given a complex geometric configuration involving points, lines, and various length(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0.03125 |
"\\triangle D F G and \\triangle F G H are isosceles, m \\angle F D H = 28 and D G \\cong F G \\cong(...TRUNCATED) | 56 | "Equals(MeasureOf(Angle(F, D, H)), 28);PointLiesOnLine(G, Line(D, H));Equals(LengthOf(Line(F, G)), L(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a geometric configuration involving several points and relationships. Let's carefully(...TRUNCATED) | ["\\boxed{We are given a geometric configuration involving several points and relationships. Let's c(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0.03125 |
In \odot F, if C F = 14 inches, what is the diameter of the circle? | 28 | "PointLiesOnLine(F, Line(A, D));PointLiesOnLine(F, Line(E, B));PointLiesOnCircle(A, Circle(F, radius(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a detailed textual description of a geometric configuration involving points, lines, (...TRUNCATED) | ["\\boxed{\\boxed{28}**}","\\boxed{We are given a detailed textual description of a geometric config(...TRUNCATED) | [1.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0(...TRUNCATED) | 0.21875 |
A B, B C, C D, and A D are tangent to a circle. If A B = 19, B C = 6, and C D = 14, find A D. | 27 | "PointLiesOnLine(I, Line(C, B));PointLiesOnLine(G, Line(D, A));PointLiesOnLine(F, Line(A, B));PointL(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a geometric configuration involving a circle tangent to four segments: AB, BC, CD, an(...TRUNCATED) | ["\\boxed{\\boxed{27}**}","\\boxed{\\boxed{27}**}","\\boxed{\\boxed{27}**}","\\boxed{\\boxed{27}**}"(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 0.96875 |
Find x. | 26 | "Equals(LengthOf(Line(B, C)), 24);Equals(LengthOf(Line(A, C)), x);Equals(LengthOf(Line(A, B)), 10);P(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given the following geometric information:\n\n- Length of segment BC is 24: \n $ BC = 24 (...TRUNCATED) | ["\\boxed{\\boxed{26}**}","\\boxed{\\boxed{26}**}","\\boxed{\\boxed{26}**}","\\boxed{\\boxed{26}**}"(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 1 |
If B E F A \sim E D C B, find x. | 4 | "Equals(LengthOf(Line(A, B)), 36);Equals(LengthOf(Line(C, D)), 12);Equals(LengthOf(Line(D, E)), x);P(...TRUNCATED) | "<|im_start|>user\n\nYou are a step-by-step reasoner for geometry problems. \nInstead of an image, y(...TRUNCATED) | ["We are given a detailed geometric description involving points, lines, perpendicularities, and a s(...TRUNCATED) | ["\\boxed{We are given a detailed geometric description involving points, lines, perpendicularities,(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0.09375 |
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