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stringlengths 34
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geometry3k/train/376/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, P)), 15); Equals(LengthOf(Line(P, Q)), 6); Equals(LengthOf(Line(P, S)), x); Equals(LengthOf(Line(T, P)), 4); PointLiesOnLine(P, Line(T, R)); PointLiesOnLine(P, Line(S, Q)); PointLiesOnCircle(T, Circle(A, radius_)); PointLiesOnCircle(S, Circle(A, radius_)); PointLiesOnCircle(R, Circle(A, radius_)); PointLiesOnCircle(Q, Circle(A, radius_)); "
}
] |
geometry3k/train/378/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, E)), 14); Equals(LengthOf(Line(B, D)), x); Equals(LengthOf(Line(A, D)), 7); PointLiesOnLine(D, Line(A, B)); PointLiesOnLine(E, Line(A, C)); PointLiesOnCircle(B, Circle(O, radius_)); PointLiesOnCircle(D, Circle(O, radius_)); PointLiesOnCircle(E, Circle(O, radius_)); "
}
] |
geometry3k/train/379/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), 26); Equals(LengthOf(Line(F, E)), 8); Equals(MeasureOf(Angle(A, G, F)), 108); Equals(LengthOf(Line(A, D)), 12); Equals(LengthOf(Line(F, G)), 14); Equals(LengthOf(Line(D, G)), 4.5); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(G, Line(D, A)); "
}
] |
geometry3k/train/380/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(1)), MeasureOf(Angle(Y, X, W))); Equals(MeasureOf(Angle(Z, X, T)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(W, T, X)), MeasureOf(Angle(3))); PointLiesOnLine(T, Line(Z, W)); PointLiesOnLine(T, Line(Y, X)); "
}
] |
geometry3k/train/382/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), x); Equals(LengthOf(Line(C, A)), y); Equals(LengthOf(Line(A, B)), 32); Equals(MeasureOf(Angle(C, A, B)), 60); Perpendicular(Line(C, B), Line(A, C)); "
}
] |
geometry3k/train/383/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), 4); Equals(LengthOf(Line(C, D)), 2); Equals(LengthOf(Line(B, E)), 3); Equals(LengthOf(Line(A, E)), x); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(C, Line(B, D)); PointLiesOnCircle(A, Circle(X, radius_)); PointLiesOnCircle(C, Circle(X, radius_)); PointLiesOnCircle(D, Circle(X, radius_)); PointLiesOnCircle(E, Circle(X, radius_)); "
}
] |
geometry3k/train/384/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(D, Line(B, C)); PointLiesOnLine(S, Line(B, C)); PointLiesOnLine(D, Line(S, C)); PointLiesOnLine(S, Line(B, D)); PointLiesOnLine(C, Line(B, R)); PointLiesOnLine(D, Line(R, B)); PointLiesOnLine(S, Line(R, B)); PointLiesOnLine(C, Line(D, R)); PointLiesOnLine(C, Line(R, S)); PointLiesOnLine(D, Line(R, S)); PointLiesOnCircle(D, Circle(R, radius_)); PointLiesOnCircle(B, Circle(S, radius_)); PointLiesOnCircle(C, Circle(S, radius_)); "
}
] |
geometry3k/train/386/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, B, E)), 60); Equals(LengthOf(Line(A, E)), y); Equals(LengthOf(Line(C, B)), LengthOf(a)); Equals(MeasureOf(Angle(B, A, C)), 30); Equals(LengthOf(Line(A, C)), LengthOf(b)); Perpendicular(Line(C, E), Line(A, E)); Perpendicular(Line(E, C), Line(A, C)); PointLiesOnLine(E, Line(A, B)); "
}
] |
geometry3k/train/388/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Parallel(Line(T, S), Line(Q, R)); PointLiesOnLine(T, Line(P, Q)); PointLiesOnLine(S, Line(P, R)); "
}
] |
geometry3k/train/389/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(J, U)), 9); Equals(LengthOf(Line(J, V)), 3); Equals(LengthOf(Line(U, T)), LengthOf(Line(T, S))); Equals(LengthOf(Line(V, Z)), LengthOf(Line(V, U))); Equals(LengthOf(Line(Z, Y)), LengthOf(Line(Y, S))); PointLiesOnLine(V, Line(Z, U)); PointLiesOnLine(Y, Line(Z, S)); PointLiesOnLine(J, Line(Z, T)); PointLiesOnLine(J, Line(Y, U)); PointLiesOnLine(T, Line(S, U)); PointLiesOnLine(J, Line(S, V)); "
}
] |
geometry3k/train/391/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, B)), 6); Equals(LengthOf(Line(B, C)), 15); Equals(LengthOf(Line(A, D)), 10); Equals(LengthOf(Line(D, E)), 3x-2); Equals(LengthOf(Line(E, C)), 12); Equals(MeasureOf(Angle(A, D, E)), MeasureOf(Angle(C, B, E))); PointLiesOnLine(E, Line(D, B)); PointLiesOnLine(E, Line(C, A)); "
}
] |
geometry3k/train/393/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(Q, Line(W, A)); PointLiesOnLine(X, Line(W, P)); PointLiesOnLine(P, Line(H, A)); PointLiesOnLine(X, Line(H, Q)); "
}
] |
geometry3k/train/398/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(U, Line(T, P)); PointLiesOnLine(A, Line(T, R)); PointLiesOnLine(Q, Line(R, P)); "
}
] |
geometry3k/train/399/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(M, F)), 8); Perpendicular(Line(H, J), Line(J, K)); PointLiesOnLine(J, Line(H, M)); PointLiesOnLine(F, Line(M, H)); PointLiesOnLine(F, Line(J, M)); PointLiesOnLine(J, Line(F, H)); PointLiesOnLine(J, Line(G, K)); PointLiesOnCircle(M, Circle(F, radius_)); PointLiesOnCircle(K, Circle(F, radius_)); PointLiesOnCircle(H, Circle(F, radius_)); PointLiesOnCircle(G, Circle(F, radius_)); "
}
] |
geometry3k/train/400/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 2\\sqrt{3}); Equals(MeasureOf(Angle(C, A, B)), 30); Equals(LengthOf(Line(Y, A)), x); Equals(LengthOf(Line(C, Y)), y); Equals(MeasureOf(Angle(A, C, B)), 60); Perpendicular(Line(C, B), Line(A, B)); Perpendicular(Line(Y, B), Line(Y, A)); PointLiesOnLine(Y, Line(C, A)); "
}
] |
geometry3k/train/401/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(F, E)), 8); Equals(LengthOf(Line(A, B)), x+1); Equals(LengthOf(Line(D, C)), x-1); Equals(LengthOf(Line(G, H)), 5); Equals(MeasureOf(Angle(D, A, B)), MeasureOf(Angle(H, E, F))); Equals(MeasureOf(Angle(C, D, A)), MeasureOf(Angle(G, H, E))); Equals(MeasureOf(Angle(F, G, H)), MeasureOf(Angle(D, C, B))); Equals(MeasureOf(Angle(E, F, G)), MeasureOf(Angle(A, B, C))); "
}
] |
geometry3k/train/403/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), 8); Equals(LengthOf(Line(C, D)), 4); Equals(LengthOf(Line(D, E)), 6); Equals(LengthOf(Line(R, S)), 3); Equals(LengthOf(Line(B, C)), LengthOf(Line(A, B))); Equals(LengthOf(Line(E, A)), LengthOf(Line(C, D))); Equals(LengthOf(Line(P, Q)), LengthOf(Line(Q, R))); Equals(LengthOf(Line(P, T)), LengthOf(Line(R, S))); "
}
] |
geometry3k/train/405/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(M, L)), 7); Equals(MeasureOf(Angle(M, L, K)), 92); PointLiesOnCircle(M, Circle(L, radius_)); "
}
] |
geometry3k/train/409/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(S, Y), Line(S, P)); Perpendicular(Line(Y, S), Line(Y, A)); Perpendicular(Line(S, Q), Line(Q, A)); PointLiesOnLine(S, Line(Q, P)); PointLiesOnLine(Y, Line(R, P)); PointLiesOnLine(A, Line(Y, X)); PointLiesOnLine(S, Line(W, Y)); PointLiesOnLine(A, Line(R, Q)); PointLiesOnLine(Q, Line(W, X)); "
}
] |
geometry3k/train/410/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Arc(W, Y)), 143); Equals(MeasureOf(Arc(Y, Z)), 2x-1); Equals(LengthOf(Line(W, Y)), 18); Equals(LengthOf(Line(Z, Y)), 18); PointLiesOnCircle(Z, Circle(O, radius_)); PointLiesOnCircle(Y, Circle(O, radius_)); PointLiesOnCircle(W, Circle(O, radius_)); "
}
] |
geometry3k/train/413/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, C, A)), 121); Equals(MeasureOf(Angle(D, C, B)), x); Equals(MeasureOf(Angle(A, C, B)), 125); PointLiesOnCircle(A, Circle(C, radius_)); PointLiesOnCircle(B, Circle(C, radius_)); PointLiesOnCircle(D, Circle(C, radius_)); "
}
] |
geometry3k/train/414/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Parallel(Line(D, E), Line(B, A)); PointLiesOnLine(E, Line(C, B)); PointLiesOnLine(D, Line(C, A)); "
}
] |
geometry3k/train/415/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(A, D, B)), 92); Equals(LengthOf(Line(A, C)), LengthOf(Line(C, B))); Equals(LengthOf(Line(D, A)), LengthOf(Line(D, C))); PointLiesOnLine(C, Line(D, B)); "
}
] |
geometry3k/train/416/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnCircle(S, Circle(D, radius_)); PointLiesOnCircle(Q, Circle(D, radius_)); PointLiesOnCircle(T, Circle(D, radius_)); "
}
] |
geometry3k/train/417/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), 54); Equals(LengthOf(Line(B, C)), x); Equals(MeasureOf(Angle(B, A, C)), 64); Equals(LengthOf(Line(A, B)), 120); "
}
] |
geometry3k/train/418/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(F, B)), x); Equals(LengthOf(Line(B, A)), y); Equals(LengthOf(Line(A, F)), z); Equals(LengthOf(Line(F, L)), 2\\sqrt{3}); Equals(LengthOf(Line(L, A)), \\sqrt{3}); Perpendicular(Line(A, B), Line(B, F)); Perpendicular(Line(A, F), Line(A, L)); PointLiesOnLine(B, Line(F, L)); "
}
] |
geometry3k/train/419/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), 16); Equals(LengthOf(Line(B, C)), 30); Equals(LengthOf(Line(A, B)), x); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/422/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), 4x-17); Equals(MeasureOf(Angle(C, B, F)), 3y+5); Equals(MeasureOf(Angle(D, F, B)), 5y-13); Equals(LengthOf(Line(D, F)), 2x-1); "
}
] |
geometry3k/train/423/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, D)), 17); Equals(LengthOf(Line(D, E)), 8); Equals(LengthOf(Line(C, A)), 21); Perpendicular(Line(A, C), Line(A, E)); Perpendicular(Line(D, E), Line(A, E)); PointLiesOnLine(E, Line(B, D)); "
}
] |
geometry3k/train/424/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(J, Line(L, N)); PointLiesOnLine(J, Line(M, P)); "
}
] |
geometry3k/train/425/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(F, B, A)), 48); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(B, A, F))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(C, F, D))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(F, D, C))); Equals(MeasureOf(Angle(E, D, F)), 39); Perpendicular(Line(B, F), Line(F, A)); Perpendicular(Line(D, C), Line(C, F)); Perpendicular(Line(F, E), Line(D, E)); Parallel(Line(D, E), Line(C, F)); PointLiesOnLine(B, Line(C, F)); PointLiesOnLine(F, Line(A, E)); "
}
] |
geometry3k/train/427/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, T)), x); Equals(LengthOf(Line(C, U)), x); Equals(LengthOf(Line(S, A)), 3); Equals(LengthOf(Line(D, R)), 3); PointLiesOnLine(C, Line(U, R)); PointLiesOnLine(B, Line(T, U)); PointLiesOnLine(A, Line(T, S)); PointLiesOnLine(D, Line(S, R)); PointLiesOnCircle(D, Circle(J, radius_)); PointLiesOnCircle(A, Circle(J, radius_)); PointLiesOnCircle(C, Circle(J, radius_)); PointLiesOnCircle(B, Circle(J, radius_)); "
}
] |
geometry3k/train/428/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, B, A)), 60); Equals(MeasureOf(Angle(A, D, C)), 45); "
}
] |
geometry3k/train/429/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 3); PointLiesOnCircle(A, Circle(B, radius_)); "
}
] |
geometry3k/train/430/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 18); Equals(LengthOf(Line(A, C)), x); Equals(MeasureOf(Angle(A, B, C)), 25); Perpendicular(Line(A, B), Line(A, C)); "
}
] |
geometry3k/train/431/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(H, E)), 8.5); Equals(MeasureOf(Angle(E, H, D)), 45); Equals(LengthOf(Line(H, G)), 15); Perpendicular(Line(G, D), Line(D, E)); PointLiesOnLine(D, Line(G, H)); "
}
] |
geometry3k/train/433/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Parallel(Line(R, Q), Line(T, P)); PointLiesOnLine(P, Line(S, Q)); PointLiesOnLine(T, Line(S, R)); "
}
] |
geometry3k/train/434/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, F, A)), 3x-15); Equals(MeasureOf(Angle(A, C, F)), y^{2}); Equals(MeasureOf(Angle(F, A, C)), 68); Equals(MeasureOf(Angle(C, E, B)), 2x); Parallel(Line(E, B), Line(F, A)); PointLiesOnLine(B, Line(F, C)); PointLiesOnLine(E, Line(A, C)); "
}
] |
geometry3k/train/435/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Parallel(Line(F, B), Line(D, C)); Parallel(Line(C, B), Line(D, F)); PointLiesOnLine(D, Line(E, C)); PointLiesOnLine(F, Line(A, E)); PointLiesOnLine(B, Line(C, A)); "
}
] |
geometry3k/train/436/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(R, S, Q)), 48); Perpendicular(Line(P, S), Line(P, Q)); Perpendicular(Line(Q, R), Line(R, S)); Equals(LengthOf(Line(P, S)), LengthOf(Line(S, R))); Equals(MeasureOf(Angle(P, Q, S)), MeasureOf(Angle(S, Q, R))); PointLiesOnLine(R, Line(Q, A)); PointLiesOnLine(P, Line(Q, B)); "
}
] |
geometry3k/train/437/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(K, A)), 4x); Equals(LengthOf(Line(G, C)), 2x); Equals(LengthOf(Line(H, A)), x); Equals(LengthOf(Line(H, C)), x); PointLiesOnLine(C, Line(J, H)); PointLiesOnLine(B, Line(J, K)); PointLiesOnLine(A, Line(H, K)); PointLiesOnCircle(B, Circle(J, radius_)); PointLiesOnCircle(C, Circle(J, radius_)); PointLiesOnCircle(A, Circle(K, radius_)); PointLiesOnCircle(B, Circle(K, radius_)); PointLiesOnCircle(A, Circle(H, radius_)); PointLiesOnCircle(C, Circle(H, radius_)); "
}
] |
geometry3k/train/439/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, A)), 12); Equals(LengthOf(Line(S, A)), x); Equals(LengthOf(Line(S, R)), 6); Equals(LengthOf(Line(S, B)), 7); Equals(LengthOf(Line(C, B)), 9); Perpendicular(Line(S, R), Line(A, S)); Perpendicular(Line(R, C), Line(C, B)); PointLiesOnLine(R, Line(C, A)); PointLiesOnLine(S, Line(B, A)); "
}
] |
geometry3k/train/440/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 15); Equals(LengthOf(Line(A, C)), 9); Equals(LengthOf(Line(B, C)), 12); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/441/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, A)), 6); Equals(LengthOf(Line(A, D)), LengthOf(Line(A, C))); Equals(LengthOf(Line(A, D)), LengthOf(Line(C, D))); Equals(LengthOf(Line(C, D)), LengthOf(Line(A, C))); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); "
}
] |
geometry3k/train/442/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(F, A, D)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(A, F, C)), 70); Equals(MeasureOf(Angle(C, E, B)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(A, B, C)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(B, C, E))); Equals(MeasureOf(Angle(E, B, F)), 35); Perpendicular(Line(A, D), Line(E, D)); Perpendicular(Line(E, B), Line(B, C)); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(E, Line(B, D)); PointLiesOnLine(F, Line(C, E)); "
}
] |
geometry3k/train/443/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(M, B, F)), 2x); Equals(MeasureOf(Angle(H, F, C)), x+10); Equals(MeasureOf(Angle(B, E, G)), x); Equals(MeasureOf(Angle(E, A, I)), x-1); Equals(MeasureOf(Angle(L, C, K)), x+18); Equals(MeasureOf(Angle(A, L, N)), 3x); PointLiesOnLine(B, Line(M, F)); PointLiesOnLine(F, Line(A, G)); PointLiesOnLine(A, Line(I, L)); PointLiesOnLine(L, Line(C, N)); PointLiesOnLine(C, Line(F, K)); PointLiesOnLine(E, Line(A, G)); "
}
] |
geometry3k/train/444/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), \\frac{3}{2}x+11); Equals(LengthOf(Line(B, D)), 3y-9); Equals(LengthOf(Line(D, A)), x+2); Equals(LengthOf(Line(D, Y)), 2x+6); Equals(LengthOf(Line(D, Y)), LengthOf(Line(D, B))); Equals(LengthOf(Line(C, A)), LengthOf(Line(Y, A))); PointLiesOnLine(A, Line(C, Y)); PointLiesOnLine(D, Line(Y, B)); "
}
] |
geometry3k/train/445/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, C)), 15); Equals(LengthOf(Line(D, A)), 6); Equals(LengthOf(Line(B, A)), 17); Perpendicular(Line(A, D), Line(C, D)); Perpendicular(Line(A, D), Line(A, B)); "
}
] |
geometry3k/train/446/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, A, F)), 20); Equals(LengthOf(Line(D, A)), 9); Equals(MeasureOf(Angle(B, A, F)), 32); Equals(LengthOf(Line(B, A)), 6); Equals(LengthOf(Line(D, C)), 6.86); Equals(MeasureOf(Angle(F, B, C)), 40.1); PointLiesOnLine(F, Line(B, D)); PointLiesOnLine(F, Line(A, C)); "
}
] |
geometry3k/train/448/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(F, B, E)), 26); Equals(MeasureOf(Arc(E, F)), x); Equals(MeasureOf(Arc(C, D)), 89); PointLiesOnLine(F, Line(B, C)); PointLiesOnLine(E, Line(B, D)); PointLiesOnCircle(C, Circle(A, radius_)); PointLiesOnCircle(D, Circle(A, radius_)); PointLiesOnCircle(E, Circle(A, radius_)); PointLiesOnCircle(F, Circle(A, radius_)); "
}
] |
geometry3k/train/450/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 9); Equals(LengthOf(Line(A, C)), x); Equals(MeasureOf(Angle(A, C, B)), 58); Equals(MeasureOf(Angle(C, B, A)), 35); "
}
] |
geometry3k/train/453/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(B, C, A)), 130); Equals(MeasureOf(Angle(B, C, D)), 60); Equals(MeasureOf(Angle(A, C, D)), x); PointLiesOnCircle(A, Circle(C, radius_)); PointLiesOnCircle(B, Circle(C, radius_)); PointLiesOnCircle(D, Circle(C, radius_)); "
}
] |
geometry3k/train/454/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(B, Line(M, E)); PointLiesOnLine(B, Line(N, P)); PointLiesOnLine(P, Line(N, G)); PointLiesOnLine(B, Line(N, G)); PointLiesOnLine(P, Line(G, B)); PointLiesOnCircle(M, Circle(P, radius_)); PointLiesOnCircle(E, Circle(P, radius_)); PointLiesOnCircle(N, Circle(P, radius_)); PointLiesOnCircle(G, Circle(P, radius_)); "
}
] |
geometry3k/train/455/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), x); Equals(LengthOf(Line(A, C)), 9); Equals(LengthOf(Line(A, B)), 18); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/456/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, A)), 13); Equals(LengthOf(Line(D, A)), 11); Equals(LengthOf(Line(B, E)), x); Perpendicular(Line(B, C), Line(E, A)); PointLiesOnLine(E, Line(C, D)); "
}
] |
geometry3k/train/457/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, D)), y); Equals(MeasureOf(Angle(B, D, A)), 60); Equals(LengthOf(Line(B, A)), 18); Equals(LengthOf(Line(D, B)), z); Equals(MeasureOf(Angle(A, B, C)), 45); Equals(LengthOf(Line(B, C)), x); Perpendicular(Line(B, A), Line(D, A)); Perpendicular(Line(C, B), Line(C, A)); "
}
] |
geometry3k/train/461/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), 10); Equals(LengthOf(Line(C, A)), x); Equals(MeasureOf(Angle(C, B, A)), 45); Equals(LengthOf(Line(C, B)), y); Perpendicular(Line(B, C), Line(C, A)); "
}
] |
geometry3k/train/463/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), 5.6); Equals(MeasureOf(Angle(B, C, A)), x); Equals(LengthOf(Line(A, B)), 6.5); Equals(LengthOf(Line(A, C)), 1.8); "
}
] |
geometry3k/train/464/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(G, F, H)), 130); Perpendicular(Line(F, H), Line(J, F)); PointLiesOnCircle(J, Circle(F, radius_)); PointLiesOnCircle(H, Circle(F, radius_)); PointLiesOnCircle(G, Circle(F, radius_)); "
}
] |
geometry3k/train/465/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, E)), 3y+4); Equals(LengthOf(Line(C, E)), 4y); Equals(LengthOf(Line(B, E)), \\frac{2}{3}x); Equals(LengthOf(Line(A, E)), x); PointLiesOnLine(E, Line(A, D)); PointLiesOnLine(E, Line(B, C)); "
}
] |
geometry3k/train/466/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, E)), 4); Equals(LengthOf(Line(B, E)), 3); PointLiesOnLine(E, Line(B, D)); PointLiesOnLine(E, Line(C, A)); "
}
] |
geometry3k/train/468/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(E, G, A)), 55); Equals(MeasureOf(Angle(E, B, H)), y); Equals(MeasureOf(Angle(A, G, B)), x); Parallel(Line(D, B), Line(A, G)); PointLiesOnLine(G, Line(A, C)); PointLiesOnLine(B, Line(F, G)); PointLiesOnLine(G, Line(B, E)); PointLiesOnLine(B, Line(D, H)); PointLiesOnLine(B, Line(F, E)); PointLiesOnLine(G, Line(E, F)); "
}
] |
geometry3k/train/469/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(M, C, N)), 60); Equals(MeasureOf(Angle(L, C, R)), 3x+5); Equals(MeasureOf(Angle(M, C, R)), x-1); PointLiesOnLine(C, Line(M, L)); PointLiesOnCircle(M, Circle(C, radius_)); PointLiesOnCircle(N, Circle(C, radius_)); PointLiesOnCircle(L, Circle(C, radius_)); PointLiesOnCircle(R, Circle(C, radius_)); "
}
] |
geometry3k/train/470/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, C)), 7); Equals(LengthOf(Line(E, D)), x); Perpendicular(Line(E, C), Line(E, D)); Perpendicular(Line(D, B), Line(C, B)); PointLiesOnCircle(B, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); "
}
] |
geometry3k/train/471/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, B)), 4); Equals(LengthOf(Line(E, F)), 14); Equals(LengthOf(Line(C, A)), 8); Perpendicular(Line(F, E), Line(F, A)); PointLiesOnLine(E, Line(D, B)); PointLiesOnLine(F, Line(A, C)); "
}
] |
geometry3k/train/472/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, D)), 19); Equals(LengthOf(Line(A, B)), 35); "
}
] |
geometry3k/train/473/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(R, S, T)), 63); PointLiesOnCircle(S, Circle(A, radius_)); PointLiesOnCircle(T, Circle(A, radius_)); "
}
] |
geometry3k/train/474/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Arc(C, Y)), 3x-3); Equals(MeasureOf(Angle(B, P, Y)), 3x); Equals(MeasureOf(Arc(A, C)), 2x+15); PointLiesOnLine(P, Line(Y, X)); PointLiesOnLine(P, Line(B, A)); PointLiesOnCircle(Y, Circle(P, radius_)); PointLiesOnCircle(B, Circle(P, radius_)); PointLiesOnCircle(X, Circle(P, radius_)); PointLiesOnCircle(A, Circle(P, radius_)); PointLiesOnCircle(C, Circle(P, radius_)); "
}
] |
geometry3k/train/475/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, Y, F)), 4y+10); PointLiesOnLine(Y, Line(B, F)); PointLiesOnLine(H, Line(Y, J)); PointLiesOnLine(H, Line(D, J)); PointLiesOnLine(Y, Line(D, J)); PointLiesOnLine(Y, Line(H, D)); PointLiesOnLine(H, Line(E, A)); "
}
] |
geometry3k/train/477/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), 32); Equals(LengthOf(Line(D, B)), y); Equals(MeasureOf(Angle(C, A, B)), 54); Equals(LengthOf(Line(D, C)), x); Perpendicular(Line(D, A), Line(D, B)); Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C))); PointLiesOnLine(D, Line(C, A)); "
}
] |
geometry3k/train/478/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(E, X), Line(E, D)); Perpendicular(Line(A, D), Line(X, A)); PointLiesOnLine(Q, Line(X, D)); PointLiesOnLine(D, Line(T, X)); PointLiesOnLine(Q, Line(T, X)); PointLiesOnLine(D, Line(T, Q)); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(E, Circle(D, radius_)); PointLiesOnCircle(T, Circle(D, radius_)); PointLiesOnCircle(Q, Circle(D, radius_)); "
}
] |
geometry3k/train/479/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, B, I)), 84); Equals(MeasureOf(Angle(I, B, H)), 16); Equals(MeasureOf(Angle(D, B, H)), x); Perpendicular(Line(B, C), Line(B, D)); PointLiesOnCircle(C, Circle(B, radius_)); PointLiesOnCircle(D, Circle(B, radius_)); PointLiesOnCircle(H, Circle(B, radius_)); PointLiesOnCircle(I, Circle(B, radius_)); "
}
] |
geometry3k/train/481/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(R, S, Q)), 5x+4); Equals(MeasureOf(Angle(S, Q, T)), 32); Equals(MeasureOf(Angle(R, T, Q)), 6x-2); PointLiesOnLine(A, Line(S, Q)); PointLiesOnLine(A, Line(R, T)); PointLiesOnCircle(S, Circle(C, radius_)); PointLiesOnCircle(R, Circle(C, radius_)); PointLiesOnCircle(T, Circle(C, radius_)); PointLiesOnCircle(Q, Circle(C, radius_)); "
}
] |
geometry3k/train/482/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(X, W), Line(W, Z)); PointLiesOnLine(A, Line(X, Z)); PointLiesOnLine(A, Line(W, Y)); "
}
] |
geometry3k/train/483/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, C)), y+8); Equals(MeasureOf(Angle(C, D, A)), 4x); Equals(MeasureOf(Angle(D, A, B)), 2x-6); Equals(LengthOf(Line(A, B)), 5y); "
}
] |
geometry3k/train/484/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, F)), 12); Equals(LengthOf(Line(F, B)), x); Equals(LengthOf(Line(B, E)), 16); Equals(LengthOf(Line(D, E)), 16); PointLiesOnLine(F, Line(B, C)); PointLiesOnLine(A, Line(C, D)); PointLiesOnLine(E, Line(B, D)); PointLiesOnCircle(A, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); PointLiesOnCircle(F, Circle(C, radius_)); "
}
] |
geometry3k/train/485/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, G)), 7); PointLiesOnLine(F, Line(A, D)); PointLiesOnLine(I, Line(A, E)); PointLiesOnLine(G, Line(D, C)); PointLiesOnLine(H, Line(E, C)); PointLiesOnCircle(F, Circle(B, radius_)); PointLiesOnCircle(G, Circle(B, radius_)); PointLiesOnCircle(H, Circle(B, radius_)); PointLiesOnCircle(I, Circle(B, radius_)); "
}
] |
geometry3k/train/486/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(B, C, D)), MeasureOf(Angle(10))); Equals(MeasureOf(Angle(B, C, E)), MeasureOf(Angle(9))); PointLiesOnLine(C, Line(A, B)); PointLiesOnLine(C, Line(D, E)); "
}
] |
geometry3k/train/487/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(T, Q)), 3x-8); Equals(LengthOf(Line(T, S)), x+10); PointLiesOnLine(Q, Line(C, T)); PointLiesOnLine(S, Line(T, E)); PointLiesOnCircle(S, Circle(B, radius_)); PointLiesOnCircle(R, Circle(B, radius_)); PointLiesOnCircle(R, Circle(A, radius_)); PointLiesOnCircle(Q, Circle(A, radius_)); "
}
] |
geometry3k/train/488/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, P)), 3); Perpendicular(Line(Q, R), Line(P, R)); PointLiesOnLine(R, Line(Q, S)); PointLiesOnCircle(Q, Circle(P, radius_)); PointLiesOnCircle(S, Circle(P, radius_)); "
}
] |
geometry3k/train/489/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), 18); Equals(LengthOf(Line(C, E)), 13); Equals(LengthOf(Line(E, D)), 24); Perpendicular(Line(C, E), Line(E, D)); "
}
] |
geometry3k/train/490/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, C)), 3y); Equals(LengthOf(Line(B, C)), 2x); Equals(LengthOf(Line(A, D)), 5x-18); Equals(LengthOf(Line(A, B)), 96-y); "
}
] |
geometry3k/train/491/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(F, A)), 24); Equals(LengthOf(Line(A, H)), 25); Equals(MeasureOf(Angle(G, C, H)), 28); Equals(LengthOf(Line(B, H)), 11); Equals(MeasureOf(Angle(A, B, H)), 30); Perpendicular(Line(H, F), Line(F, A)); Perpendicular(Line(H, D), Line(D, B)); Perpendicular(Line(G, H), Line(G, B)); PointLiesOnLine(F, Line(C, A)); PointLiesOnLine(G, Line(B, C)); PointLiesOnLine(D, Line(A, B)); "
}
] |
geometry3k/train/498/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(E, D, C)), 57); PointLiesOnCircle(E, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); "
}
] |
geometry3k/train/499/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(A, Line(P, N)); PointLiesOnLine(A, Line(M, O)); "
}
] |
geometry3k/train/500/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(B, A, D)), 3x); Equals(MeasureOf(Angle(A, D, C)), x); Perpendicular(Line(B, C), Line(A, B)); Perpendicular(Line(D, C), Line(B, C)); "
}
] |
geometry3k/train/501/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, B, L)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(F, B, D)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(M, F, B))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(L, B, G))); Equals(MeasureOf(Angle(6)), MeasureOf(Angle(M, F, T))); Equals(MeasureOf(Angle(J, B, G)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(E, J, B)), MeasureOf(Angle(9))); Equals(MeasureOf(Angle(E, J, T)), MeasureOf(Angle(10))); Equals(MeasureOf(Angle(I, F, B)), MeasureOf(Angle(8))); Equals(MeasureOf(Angle(7)), MeasureOf(Angle(I, F, J))); Equals(MeasureOf(Angle(11)), MeasureOf(Angle(C, J, T))); Equals(MeasureOf(Angle(12)), MeasureOf(Angle(C, J, L))); Parallel(Line(G, D), Line(M, I)); Parallel(Line(D, G), Line(E, C)); PointLiesOnLine(J, Line(F, T)); PointLiesOnLine(B, Line(F, L)); PointLiesOnLine(F, Line(I, M)); PointLiesOnLine(F, Line(T, B)); PointLiesOnLine(J, Line(T, B)); PointLiesOnLine(F, Line(J, B)); PointLiesOnLine(B, Line(D, G)); PointLiesOnLine(B, Line(L, T)); PointLiesOnLine(F, Line(L, T)); PointLiesOnLine(J, Line(T, L)); PointLiesOnLine(B, Line(L, J)); PointLiesOnLine(F, Line(L, J)); PointLiesOnLine(J, Line(E, C)); "
}
] |
geometry3k/train/502/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(J, K, L)), 62); PointLiesOnLine(A, Line(L, K)); PointLiesOnCircle(L, Circle(A, radius_)); PointLiesOnCircle(J, Circle(A, radius_)); PointLiesOnCircle(K, Circle(A, radius_)); "
}
] |
geometry3k/train/503/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, D)), x); Equals(LengthOf(Line(C, A)), y); Equals(LengthOf(Line(D, B)), 12.5); Equals(LengthOf(Line(D, A)), 8); Equals(LengthOf(Line(B, C)), z); Perpendicular(Line(C, B), Line(C, A)); Perpendicular(Line(C, D), Line(D, B)); PointLiesOnLine(D, Line(A, B)); "
}
] |
geometry3k/train/506/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(N, Line(D, A)); PointLiesOnCircle(D, Circle(N, radius_)); PointLiesOnCircle(A, Circle(N, radius_)); PointLiesOnCircle(B, Circle(N, radius_)); PointLiesOnCircle(C, Circle(N, radius_)); PointLiesOnCircle(E, Circle(N, radius_)); "
}
] |
geometry3k/train/507/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, B)), 3y-6); Equals(LengthOf(Line(B, F)), 2y+4); Equals(LengthOf(Line(F, G)), \\frac{1}{2}x+12); Equals(LengthOf(Line(D, G)), \\frac{3}{2}x+8); PointLiesOnLine(G, Line(D, F)); PointLiesOnLine(B, Line(E, F)); "
}
] |
geometry3k/train/509/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(J, K, L)), 70); Equals(LengthOf(Line(L, J)), LengthOf(Line(K, L))); "
}
] |
geometry3k/train/510/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(C, D), Line(E, D)); Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C))); Equals(LengthOf(Line(B, C)), LengthOf(Line(A, C))); "
}
] |
geometry3k/train/512/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, D)), 6); Equals(LengthOf(Line(E, C)), 12-x); Equals(LengthOf(Line(A, C)), x+7); Equals(LengthOf(Line(B, C)), 4); Perpendicular(Line(A, B), Line(D, B)); Perpendicular(Line(D, B), Line(E, D)); PointLiesOnLine(C, Line(D, B)); PointLiesOnLine(C, Line(E, A)); "
}
] |
geometry3k/train/515/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(F, R)), 2); Equals(LengthOf(Line(E, R)), r); Equals(LengthOf(Line(D, F)), 16); Equals(LengthOf(Line(E, A)), 18.5); Equals(LengthOf(Line(D, B)), 9); Equals(LengthOf(Line(A, B)), 15); PointLiesOnLine(E, Line(R, A)); PointLiesOnLine(D, Line(B, R)); PointLiesOnLine(F, Line(R, B)); PointLiesOnLine(F, Line(D, R)); PointLiesOnLine(D, Line(F, B)); PointLiesOnCircle(A, Circle(C, radius_)); PointLiesOnCircle(D, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); PointLiesOnCircle(F, Circle(C, radius_)); PointLiesOnCircle(G, Circle(C, radius_)); PointLiesOnCircle(H, Circle(C, radius_)); "
}
] |
geometry3k/train/516/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, N)), 9); Equals(LengthOf(Line(M, O)), 16); "
}
] |
geometry3k/train/518/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, D)), 5y); Equals(LengthOf(Line(E, B)), \\frac{7}{3}y+8); Equals(LengthOf(Line(A, D)), \\frac{1}{3}x+2); Equals(LengthOf(Line(A, C)), \\frac{2}{3}x-4); Equals(LengthOf(Line(C, A)), LengthOf(Line(D, A))); Equals(LengthOf(Line(D, E)), LengthOf(Line(E, B))); PointLiesOnLine(A, Line(C, D)); PointLiesOnLine(E, Line(D, B)); "
}
] |
geometry3k/train/519/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), z); Equals(LengthOf(Line(B, D)), 8); Equals(LengthOf(Line(B, A)), y); Equals(MeasureOf(Angle(B, A, C)), 45); Equals(MeasureOf(Angle(A, D, B)), 60); Equals(LengthOf(Line(D, A)), x); Perpendicular(Line(C, B), Line(C, A)); Perpendicular(Line(D, A), Line(A, B)); "
}
] |
geometry3k/train/520/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(B, Line(L, P)); PointLiesOnLine(B, Line(Q, M)); PointLiesOnCircle(L, Circle(B, radius_)); PointLiesOnCircle(M, Circle(B, radius_)); PointLiesOnCircle(K, Circle(B, radius_)); PointLiesOnCircle(P, Circle(B, radius_)); PointLiesOnCircle(Q, Circle(B, radius_)); "
}
] |
geometry3k/train/521/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, A, B)), 4x-26); Equals(MeasureOf(Angle(A, B, C)), x); Equals(MeasureOf(Angle(C, D, A)), x); Equals(MeasureOf(Angle(B, C, D)), 2x+18); "
}
] |
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