problem
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stringlengths 1
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| description
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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
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|---|---|---|---|---|---|---|---|
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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