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geometry3k/train/671/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(R, P)); "
}
] |
geometry3k/train/672/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, B)), 3y-4); Equals(MeasureOf(Angle(D, C, F)), 54); Equals(LengthOf(Line(C, D)), 25); Equals(LengthOf(Line(B, A)), 5x); Equals(MeasureOf(Angle(F, A, D)), 49); Equals(MeasureOf(Angle(A, D, B)), 34); Equals(LengthOf(Line(D, A)), 29); PointLiesOnLine(F, Line(B, D)); PointLiesOnLine(F, Line(A, C)); "
}
] |
geometry3k/train/673/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(E, Line(B, D)); PointLiesOnLine(E, Line(A, C)); PointLiesOnCircle(B, Circle(E, radius_)); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); "
}
] |
geometry3k/train/676/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(T, F)), 12); Equals(LengthOf(Line(A, F)), LengthOf(Line(E, A))); Equals(LengthOf(Line(F, C)), LengthOf(Line(D, C))); Equals(LengthOf(Line(E, Q)), LengthOf(Line(D, Q))); PointLiesOnLine(T, Line(A, D)); PointLiesOnLine(C, Line(D, F)); PointLiesOnLine(Q, Line(D, E)); PointLiesOnLine(T, Line(F, Q)); PointLiesOnLine(A, Line(F, E)); PointLiesOnLine(T, Line(C, E)); "
}
] |
geometry3k/train/677/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, K)), 2b+3); Equals(LengthOf(Line(J, M)), 3a); Equals(LengthOf(Line(L, K)), 21); Equals(MeasureOf(Angle(R, L, K)), 70); Equals(MeasureOf(Angle(J, L, M)), 30); Equals(LengthOf(Line(L, M)), 45); PointLiesOnLine(R, Line(J, L)); PointLiesOnLine(R, Line(K, M)); "
}
] |
geometry3k/train/678/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, D)), 5.3); Perpendicular(Line(B, D), Line(D, C)); Perpendicular(Line(B, C), Line(A, B)); PointLiesOnLine(D, Line(A, C)); "
}
] |
geometry3k/train/679/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)), 10.2); Equals(LengthOf(Line(A, C)), x); Equals(LengthOf(Line(B, C)), 6.3); Perpendicular(Line(A, B), Line(B, C)); "
}
] |
geometry3k/train/680/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, X)), 5); Equals(LengthOf(Line(A, Y)), 9); Perpendicular(Line(Z, A), Line(A, X)); Perpendicular(Line(Z, Y), Line(Z, A)); PointLiesOnLine(A, Line(X, Y)); "
}
] |
geometry3k/train/681/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(L, K, J)), 109); Equals(LengthOf(Line(L, M)), 6); "
}
] |
geometry3k/train/682/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(V, X, V)), 14); PointLiesOnLine(F, Line(X, W)); PointLiesOnCircle(X, Circle(F, radius_)); PointLiesOnCircle(V, Circle(F, radius_)); PointLiesOnCircle(W, Circle(F, radius_)); "
}
] |
geometry3k/train/683/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)), x+15); Equals(LengthOf(Line(B, E)), x); Perpendicular(Line(B, E), Line(C, E)); PointLiesOnLine(E, Line(D, C)); "
}
] |
geometry3k/train/687/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, J)), 3); Equals(MeasureOf(Arc(C, E)), 5x-6); Equals(MeasureOf(Arc(C, J)), 4x+8); PointLiesOnLine(J, Line(B, E)); PointLiesOnCircle(E, Circle(H, radius_)); PointLiesOnCircle(J, Circle(H, radius_)); PointLiesOnCircle(C, Circle(H, radius_)); "
}
] |
geometry3k/train/688/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, C)), 7); Equals(LengthOf(Line(M, R)), 4); Equals(LengthOf(Line(A, S)), LengthOf(Line(B, S))); Equals(LengthOf(Line(T, C)), LengthOf(Line(B, T))); Equals(LengthOf(Line(C, R)), LengthOf(Line(A, R))); PointLiesOnLine(M, Line(S, C)); PointLiesOnLine(T, Line(B, C)); PointLiesOnLine(R, Line(C, A)); PointLiesOnLine(S, Line(A, B)); PointLiesOnLine(M, Line(R, B)); PointLiesOnLine(M, Line(T, A)); "
}
] |
geometry3k/train/690/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, Q)), 8); Equals(LengthOf(Line(W, X)), 4); Equals(LengthOf(Line(N, P)), 10); Equals(LengthOf(Line(M, N)), 9); Equals(LengthOf(Line(Q, P)), 7); "
}
] |
geometry3k/train/694/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, A, B)), 80); Equals(LengthOf(Line(A, B)), 4y-2); Equals(LengthOf(Line(C, A)), 2y+2); Equals(MeasureOf(Angle(A, C, B)), 6x+8); Equals(LengthOf(Line(A, C)), LengthOf(Line(B, A))); "
}
] |
geometry3k/train/697/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(L, K)), 3y); Equals(LengthOf(Line(J, L)), 7); Equals(LengthOf(Line(L, M)), 9x); Equals(LengthOf(Line(N, K)), 36); Equals(LengthOf(Line(N, J)), y+15); PointLiesOnLine(J, Line(K, M)); PointLiesOnLine(J, Line(N, L)); "
}
] |
geometry3k/train/698/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(T, V, S)), 75); Equals(MeasureOf(Angle(P, V, T)), 72); Perpendicular(Line(R, V), Line(S, V)); PointLiesOnLine(V, Line(S, Q)); PointLiesOnCircle(S, Circle(V, radius_)); PointLiesOnCircle(P, Circle(V, radius_)); PointLiesOnCircle(R, Circle(V, radius_)); PointLiesOnCircle(T, Circle(V, radius_)); PointLiesOnCircle(Q, Circle(V, radius_)); "
}
] |
geometry3k/train/699/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(X, O)), x+4); Equals(LengthOf(Line(O, W)), x-9); Equals(LengthOf(Line(O, Y)), x); Equals(LengthOf(Line(Z, O)), x-12); PointLiesOnLine(O, Line(Z, X)); PointLiesOnLine(O, Line(Y, W)); PointLiesOnCircle(Z, Circle(A, radius_)); PointLiesOnCircle(Y, Circle(A, radius_)); PointLiesOnCircle(X, Circle(A, radius_)); PointLiesOnCircle(W, Circle(A, radius_)); "
}
] |
geometry3k/train/703/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, D)), LengthOf(Line(B, C))); PointLiesOnLine(P, Line(A, C)); PointLiesOnLine(P, Line(B, D)); "
}
] |
geometry3k/train/704/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(K, J)), 3f-6); Equals(MeasureOf(Angle(K, J, M)), 56); Equals(MeasureOf(Angle(J, M, L)), 3d-2); Equals(LengthOf(Line(L, M)), 2f+8); "
}
] |
geometry3k/train/705/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)), 12); Equals(LengthOf(h), LengthOf(Line(C, A))); Equals(MeasureOf(Angle(A, B, C)), 30); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/708/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, G)), 16); PointLiesOnCircle(A, Circle(G, radius_)); PointLiesOnCircle(C, Circle(G, radius_)); PointLiesOnCircle(D, Circle(G, radius_)); PointLiesOnCircle(E, Circle(G, radius_)); PointLiesOnCircle(F, Circle(G, radius_)); PointLiesOnCircle(H, Circle(G, radius_)); "
}
] |
geometry3k/train/710/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, H)), 11); "
}
] |
geometry3k/train/711/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)), 15); Equals(MeasureOf(Angle(B, D, E)), 82); Equals(LengthOf(Line(E, F)), 9.2); PointLiesOnLine(F, Line(C, A)); PointLiesOnLine(E, Line(C, B)); PointLiesOnLine(D, Line(B, A)); "
}
] |
geometry3k/train/712/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)), 6); Equals(MeasureOf(Angle(C, A, B)), 45); Equals(LengthOf(Line(A, B)), x); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/715/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(G, C)), 12.25); Equals(LengthOf(Line(A, G)), y); Equals(LengthOf(Line(F, A)), 2x); Equals(LengthOf(Line(B, F)), 24); Equals(LengthOf(Line(C, D)), 9); Equals(LengthOf(Line(B, D)), x); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(G, Line(C, A)); PointLiesOnLine(B, Line(A, D)); PointLiesOnLine(F, Line(D, A)); PointLiesOnLine(B, Line(F, D)); PointLiesOnCircle(B, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); PointLiesOnCircle(G, Circle(E, radius_)); "
}
] |
geometry3k/train/719/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(W, Y)); PointLiesOnLine(U, Line(Z, X)); "
}
] |
geometry3k/train/721/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(J, R), Line(H, S)); Parallel(Line(K, Q), Line(H, S)); Parallel(Line(L, P), Line(Q, K)); PointLiesOnLine(K, Line(M, H)); PointLiesOnLine(K, Line(J, M)); PointLiesOnLine(K, Line(L, H)); PointLiesOnLine(K, Line(J, L)); PointLiesOnLine(J, Line(H, M)); PointLiesOnLine(J, Line(K, H)); PointLiesOnLine(J, Line(L, H)); PointLiesOnLine(L, Line(M, H)); PointLiesOnLine(L, Line(M, K)); PointLiesOnLine(L, Line(M, J)); PointLiesOnLine(Q, Line(S, M)); PointLiesOnLine(Q, Line(M, R)); PointLiesOnLine(Q, Line(P, S)); PointLiesOnLine(Q, Line(R, P)); PointLiesOnLine(R, Line(M, S)); PointLiesOnLine(R, Line(S, Q)); PointLiesOnLine(R, Line(P, S)); PointLiesOnLine(P, Line(S, M)); PointLiesOnLine(P, Line(M, Q)); PointLiesOnLine(P, Line(R, M)); "
}
] |
geometry3k/train/724/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(H, C, A)), x-10); Equals(MeasureOf(Angle(G, M, O)), 104); Parallel(Line(D, H), Line(J, O)); PointLiesOnLine(M, Line(G, A)); PointLiesOnLine(M, Line(J, O)); PointLiesOnLine(M, Line(G, C)); PointLiesOnLine(C, Line(A, G)); PointLiesOnLine(C, Line(A, M)); PointLiesOnLine(C, Line(D, H)); "
}
] |
geometry3k/train/725/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, P)), 8); Perpendicular(Line(C, B), Line(C, P)); Perpendicular(Line(P, A), Line(A, B)); Equals(MeasureOf(Angle(C, B, P)), MeasureOf(Angle(P, B, A))); PointLiesOnLine(A, Line(Y, B)); PointLiesOnLine(C, Line(B, D)); PointLiesOnLine(P, Line(E, B)); "
}
] |
geometry3k/train/728/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(Z, X, V)), 2x+65); Equals(MeasureOf(Angle(Y, X, W)), 4x+15); PointLiesOnLine(X, Line(W, Z)); PointLiesOnLine(X, Line(Y, V)); PointLiesOnCircle(W, Circle(X, radius_)); PointLiesOnCircle(Y, Circle(X, radius_)); PointLiesOnCircle(V, Circle(X, radius_)); PointLiesOnCircle(Z, Circle(X, radius_)); "
}
] |
geometry3k/train/729/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(F, C), Line(F, E)); PointLiesOnLine(F, Line(C, A)); PointLiesOnLine(F, Line(E, D)); PointLiesOnLine(C, Line(F, B)); PointLiesOnLine(C, Line(A, B)); PointLiesOnLine(F, Line(B, A)); PointLiesOnCircle(D, Circle(C, radius_)); PointLiesOnCircle(B, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); PointLiesOnCircle(A, Circle(C, radius_)); "
}
] |
geometry3k/train/730/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(E, F), Line(H, L)); PointLiesOnLine(L, Line(G, F)); PointLiesOnLine(H, Line(G, E)); "
}
] |
geometry3k/train/731/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, F)), 53); Equals(MeasureOf(Angle(E, C, B)), MeasureOf(Angle(2))); PointLiesOnLine(C, Line(B, F)); PointLiesOnLine(C, Line(D, E)); "
}
] |
geometry3k/train/732/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)), y); Equals(LengthOf(Line(A, B)), x); Equals(MeasureOf(Angle(A, C, B)), 60); Equals(LengthOf(Line(A, C)), 12); Perpendicular(Line(B, A), Line(B, C)); "
}
] |
geometry3k/train/733/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(A, D, F)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(G, D, F))); Equals(MeasureOf(Angle(E, D, G)), MeasureOf(Angle(5))); Perpendicular(Line(A, D), Line(H, D)); PointLiesOnLine(D, Line(E, A)); PointLiesOnLine(D, Line(F, H)); "
}
] |
geometry3k/train/734/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, H)), 3r); PointLiesOnLine(D, Line(A, C)); PointLiesOnLine(J, Line(A, F)); PointLiesOnLine(I, Line(C, E)); PointLiesOnLine(B, Line(F, E)); PointLiesOnCircle(B, Circle(H, radius_)); PointLiesOnCircle(D, Circle(H, radius_)); PointLiesOnCircle(I, Circle(H, radius_)); PointLiesOnCircle(J, Circle(H, radius_)); "
}
] |
geometry3k/train/735/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(P, Line(S, Q)); PointLiesOnLine(P, Line(R, T)); "
}
] |
geometry3k/train/739/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(X, C, D)), 18); Equals(LengthOf(Line(C, D)), 22); Equals(MeasureOf(Angle(X, D, C)), 105); "
}
] |
geometry3k/train/741/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)), 10); Equals(LengthOf(Line(J, H)), x); "
}
] |
geometry3k/train/743/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(C, B), Line(E, D)); PointLiesOnLine(B, Line(E, A)); PointLiesOnLine(C, Line(A, D)); "
}
] |
geometry3k/train/744/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, H)), 10); Equals(LengthOf(Line(H, K)), 5); Equals(LengthOf(Line(E, I)), 5); Equals(LengthOf(Line(I, B)), 7); Equals(LengthOf(Line(K, A)), 7); Equals(LengthOf(Line(B, L)), 5); Equals(LengthOf(Line(A, G)), 5); Equals(LengthOf(Line(L, F)), 7); Equals(LengthOf(Line(G, D)), 7); Equals(LengthOf(Line(F, C)), 5); Equals(LengthOf(Line(J, D)), 5); Equals(LengthOf(Line(C, J)), 10); Perpendicular(Line(H, E), Line(E, I)); Perpendicular(Line(E, H), Line(H, K)); Perpendicular(Line(B, I), Line(I, E)); Perpendicular(Line(H, K), Line(K, A)); Perpendicular(Line(B, L), Line(I, B)); Perpendicular(Line(K, A), Line(G, A)); Perpendicular(Line(L, B), Line(F, L)); Perpendicular(Line(D, G), Line(G, A)); Perpendicular(Line(F, C), Line(F, L)); Perpendicular(Line(D, G), Line(J, D)); Perpendicular(Line(C, F), Line(J, C)); Perpendicular(Line(J, D), Line(J, C)); PointLiesOnLine(K, Line(B, A)); PointLiesOnLine(B, Line(I, A)); PointLiesOnLine(K, Line(A, I)); PointLiesOnLine(D, Line(F, G)); PointLiesOnLine(L, Line(G, F)); PointLiesOnLine(D, Line(L, G)); PointLiesOnLine(F, Line(C, I)); PointLiesOnLine(B, Line(K, I)); PointLiesOnLine(D, Line(K, J)); PointLiesOnLine(F, Line(E, C)); PointLiesOnLine(I, Line(C, E)); PointLiesOnLine(I, Line(F, E)); PointLiesOnLine(L, Line(F, D)); PointLiesOnLine(D, Line(J, H)); PointLiesOnLine(K, Line(J, H)); PointLiesOnLine(K, Line(H, D)); "
}
] |
geometry3k/train/745/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, B)), 15); Equals(LengthOf(Line(R, S)), 26); PointLiesOnLine(A, Line(R, V)); PointLiesOnLine(B, Line(S, T)); "
}
] |
geometry3k/train/747/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(R, Line(Z, Y)); PointLiesOnLine(Q, Line(Z, X)); "
}
] |
geometry3k/train/749/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(Y, S), Line(C, P)); Perpendicular(Line(Y, B), Line(S, Y)); Perpendicular(Line(B, Q), Line(Q, C)); PointLiesOnLine(S, Line(Y, W)); PointLiesOnLine(S, Line(P, Q)); PointLiesOnLine(Q, Line(W, X)); PointLiesOnLine(B, Line(Y, X)); PointLiesOnLine(B, Line(Q, R)); PointLiesOnLine(B, Line(R, Q)); PointLiesOnLine(Y, Line(R, P)); "
}
] |
geometry3k/train/750/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(A, B, E)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(B, E, A))); Equals(MeasureOf(Angle(B, A, E)), 15); Equals(MeasureOf(Angle(A, E, C)), 74); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(C, A, E))); Perpendicular(Line(C, A), Line(E, C)); PointLiesOnLine(E, Line(B, C)); "
}
] |
geometry3k/train/751/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(H, Line(J, G)); "
}
] |
geometry3k/train/752/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)), 17); Equals(LengthOf(Line(N, M)), 2x+7); Equals(LengthOf(Line(N, L)), 3x-4); Equals(LengthOf(Line(L, N)), LengthOf(Line(N, M))); "
}
] |
geometry3k/train/753/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(W, C, Y)), 128); Equals(MeasureOf(Arc(W, Y)), 154); Equals(MeasureOf(Arc(Z, X)), x); PointLiesOnLine(C, Line(Z, W)); PointLiesOnLine(C, Line(X, Y)); PointLiesOnCircle(Z, Circle(A, radius_)); PointLiesOnCircle(X, Circle(A, radius_)); PointLiesOnCircle(Y, Circle(A, radius_)); PointLiesOnCircle(W, Circle(A, radius_)); "
}
] |
geometry3k/train/754/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(H, F)), 12); Equals(LengthOf(Line(H, G)), 12); Perpendicular(Line(E, H), Line(G, H)); Perpendicular(Line(F, E), Line(E, G)); PointLiesOnLine(H, Line(G, F)); "
}
] |
geometry3k/train/755/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(Z, T, W)), MeasureOf(Angle(Y, W, T))); Equals(MeasureOf(Angle(T, Z, Y)), MeasureOf(Angle(Z, Y, W))); "
}
] |
geometry3k/train/756/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(T, Q, R)), 2x+5); Equals(MeasureOf(Angle(Q, R, S)), x); Equals(MeasureOf(Angle(S, T, Q)), x); Equals(MeasureOf(Angle(R, S, T)), 2x+7); "
}
] |
geometry3k/train/761/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)), x); Equals(LengthOf(Line(A, B)), 5); Equals(LengthOf(Line(B, C)), 5); Perpendicular(Line(B, C), Line(A, B)); "
}
] |
geometry3k/train/763/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, K)), 12); Equals(LengthOf(Line(P, Q)), 15); "
}
] |
geometry3k/train/764/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, F, H)), 81); PointLiesOnCircle(D, Circle(A, radius_)); PointLiesOnCircle(F, Circle(A, radius_)); PointLiesOnCircle(H, Circle(A, radius_)); "
}
] |
geometry3k/train/765/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(A, B, E)), 58); Equals(LengthOf(Line(B, C)), 4); Equals(LengthOf(Line(E, T)), LengthOf(Line(B, E))); Equals(LengthOf(Line(E, A)), LengthOf(Line(E, C))); PointLiesOnLine(E, Line(A, C)); PointLiesOnLine(E, Line(B, T)); "
}
] |
geometry3k/train/766/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(M, Line(R, S)); PointLiesOnLine(N, Line(T, V)); "
}
] |
geometry3k/train/768/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, D, A)), 90); Equals(LengthOf(Line(A, D)), 6x+1); Equals(MeasureOf(Angle(A, B, G)), 30); Equals(MeasureOf(Angle(A, B, H)), 30); Equals(LengthOf(Line(A, C)), 7x-4); Equals(MeasureOf(Angle(A, C, B)), 90); PointLiesOnLine(A, Line(B, F)); PointLiesOnLine(D, Line(B, G)); PointLiesOnLine(C, Line(B, H)); "
}
] |
geometry3k/train/770/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)), 3); Equals(LengthOf(Line(B, D)), 12); Equals(LengthOf(Line(C, A)), y); Equals(LengthOf(Line(D, C)), x); Equals(LengthOf(Line(C, B)), z); Perpendicular(Line(D, A), Line(C, D)); Perpendicular(Line(B, C), Line(C, A)); PointLiesOnLine(D, Line(A, B)); "
}
] |
geometry3k/train/772/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)), 17\\sqrt{2}); Equals(MeasureOf(Angle(C, B, A)), 45); Equals(LengthOf(Line(A, B)), x); Equals(MeasureOf(Angle(C, A, B)), 45); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/773/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, O)), 35); Equals(LengthOf(Line(A, O)), 25); Equals(LengthOf(Line(C, A)), 23); Equals(LengthOf(Line(C, B)), 11); Perpendicular(Line(A, C), Line(A, O)); PointLiesOnLine(C, Line(B, A)); "
}
] |
geometry3k/train/775/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)), 5x+21); Equals(MeasureOf(Angle(G, D, C)), 12x+6); PointLiesOnLine(C, Line(P, A)); PointLiesOnLine(D, Line(C, B)); PointLiesOnLine(C, Line(F, B)); PointLiesOnLine(D, Line(B, F)); PointLiesOnLine(C, Line(F, D)); PointLiesOnLine(D, Line(E, G)); "
}
] |
geometry3k/train/778/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)), x); Equals(MeasureOf(Angle(C, A, B)), 45); Equals(LengthOf(Line(B, C)), 6\\sqrt{2}); Perpendicular(Line(A, B), Line(B, C)); "
}
] |
geometry3k/train/779/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)), y); Equals(MeasureOf(Angle(A, C, B)), 60); Equals(LengthOf(Line(C, A)), x); Equals(LengthOf(Line(B, A)), 12); Perpendicular(Line(C, A), Line(A, B)); "
}
] |
geometry3k/train/780/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)), 14); Equals(LengthOf(Line(C, B)), 11); Equals(LengthOf(Line(D, A)), x); Equals(LengthOf(Line(A, C)), 20); Equals(MeasureOf(Angle(C, B, D)), MeasureOf(Angle(D, B, A))); PointLiesOnLine(D, Line(A, C)); "
}
] |
geometry3k/train/781/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(Z, Y, W)), 58); Equals(MeasureOf(Angle(Y, X, Z)), MeasureOf(Angle(7))); Equals(MeasureOf(Angle(Y, Z, X)), 65); Equals(MeasureOf(Angle(Z, V, W)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(V, X, W)), MeasureOf(Angle(5))); Equals(MeasureOf(Angle(Z, X, W)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(X, Z, W)), MeasureOf(Angle(9))); Equals(MeasureOf(Angle(8)), MeasureOf(Angle(X, W, Z))); Equals(MeasureOf(Angle(X, Z, W)), MeasureOf(Angle(X, W, Z))); Equals(MeasureOf(Angle(Y, W, V)), 67); PointLiesOnLine(X, Line(W, Y)); PointLiesOnLine(X, Line(Z, V)); "
}
] |
geometry3k/train/782/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(M, Line(L, J)); "
}
] |
geometry3k/train/784/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)), 17); Equals(MeasureOf(Angle(A, C, D)), 45); Equals(LengthOf(Line(C, E)), 9); Perpendicular(Line(D, E), Line(E, A)); PointLiesOnLine(E, Line(D, C)); "
}
] |
geometry3k/train/785/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)), 9); Perpendicular(Line(A, C), Line(B, C)); Perpendicular(Line(D, A), Line(A, C)); Perpendicular(Line(D, B), Line(D, A)); Perpendicular(Line(B, D), Line(C, B)); PointLiesOnLine(H, Line(C, A)); PointLiesOnLine(G, Line(D, A)); PointLiesOnLine(F, Line(C, B)); PointLiesOnLine(E, Line(D, B)); PointLiesOnCircle(E, Circle(P, radius_)); PointLiesOnCircle(F, Circle(P, radius_)); PointLiesOnCircle(G, Circle(P, radius_)); PointLiesOnCircle(H, Circle(P, radius_)); "
}
] |
geometry3k/train/789/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, E)), 12-2x); Equals(LengthOf(Line(D, A)), 7y); Equals(LengthOf(Line(E, C)), 8x-18); Equals(LengthOf(Line(A, C)), 5y+16); Equals(MeasureOf(Angle(B, D, A)), MeasureOf(Angle(E, A, C))); PointLiesOnLine(E, Line(C, B)); PointLiesOnLine(A, Line(C, D)); "
}
] |
geometry3k/train/791/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, B)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(S, A, C)), 125); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(C, A, B))); Equals(MeasureOf(Angle(C, B, A)), 62); Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(D, B, S)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(C, D, B)), 32); PointLiesOnLine(A, Line(B, S)); PointLiesOnLine(A, Line(C, D)); "
}
] |
geometry3k/train/792/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(Q, R)), 6); Equals(LengthOf(Line(W, V)), 8); Equals(LengthOf(Line(W, P)), 3); Equals(LengthOf(Line(R, T)), x); Equals(LengthOf(Line(U, T)), 4); PointLiesOnLine(U, Line(V, T)); PointLiesOnLine(S, Line(R, T)); PointLiesOnLine(W, Line(V, P)); PointLiesOnLine(Q, Line(R, P)); PointLiesOnCircle(U, Circle(Z, radius_)); PointLiesOnCircle(S, Circle(Z, radius_)); PointLiesOnCircle(Q, Circle(Z, radius_)); PointLiesOnCircle(W, Circle(Z, radius_)); "
}
] |
geometry3k/train/793/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(L, P)), 106); Equals(MeasureOf(Arc(P, M)), x); Equals(LengthOf(Line(P, M)), LengthOf(Line(L, M))); PointLiesOnCircle(L, Circle(O, radius_)); PointLiesOnCircle(M, Circle(O, radius_)); PointLiesOnCircle(P, Circle(O, radius_)); "
}
] |
geometry3k/train/794/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, J, C)), 2x); Equals(MeasureOf(Angle(J, C, A)), 96); Equals(MeasureOf(Angle(J, E, A)), 3y+44); Equals(MeasureOf(Angle(C, A, E)), 94); Parallel(Line(C, A), Line(E, J)); "
}
] |
geometry3k/train/795/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(F, Line(A, D)); PointLiesOnLine(F, Line(E, B)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(E, Circle(F, radius_)); PointLiesOnCircle(D, Circle(F, radius_)); PointLiesOnCircle(B, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); "
}
] |
geometry3k/train/796/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(V, X)), 75); Equals(LengthOf(Line(W, V)), 72); Equals(LengthOf(Line(W, X)), 21); Perpendicular(Line(W, V), Line(W, X)); "
}
] |
geometry3k/train/797/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, S)), 5); Perpendicular(Line(P, R), Line(P, Q)); Perpendicular(Line(S, Q), Line(S, S)); PointLiesOnLine(S, Line(Q, R)); "
}
] |
geometry3k/train/798/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(D, A)), 5); Equals(LengthOf(Line(A, Q)), 3+x); Equals(LengthOf(Line(P, Q)), 6-x); Equals(LengthOf(Line(Q, R)), 6+x); Equals(LengthOf(Line(T, Q)), 3); Parallel(Line(P, T), Line(S, R)); PointLiesOnLine(Q, Line(P, R)); PointLiesOnLine(D, Line(R, A)); PointLiesOnLine(Q, Line(A, T)); PointLiesOnLine(D, Line(A, B)); "
}
] |
geometry3k/train/799/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)), x); Equals(MeasureOf(Angle(B, A, C)), 60); Equals(LengthOf(Line(C, B)), 15); Equals(LengthOf(Line(B, A)), y); Perpendicular(Line(A, C), Line(C, B)); "
}
] |
geometry3k/train/800/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, S)), 12+x); Equals(LengthOf(Line(R, S)), 4x-4); Equals(LengthOf(Line(T, R)), 3x+3); Equals(LengthOf(Line(R, S)), LengthOf(Line(T, R))); "
}
] |
geometry3k/train/802/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": ""
}
] |
geometry3k/train/803/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)), 35); Equals(LengthOf(Line(C, D)), 25); "
}
] |
geometry3k/train/804/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(H, F)), 8); Perpendicular(Line(H, J), Line(H, F)); Perpendicular(Line(F, L), Line(L, K)); PointLiesOnLine(L, Line(M, K)); PointLiesOnLine(F, Line(K, G)); PointLiesOnLine(F, Line(H, L)); PointLiesOnLine(H, Line(J, G)); PointLiesOnCircle(K, Circle(F, radius_)); PointLiesOnCircle(M, Circle(F, radius_)); PointLiesOnCircle(G, Circle(F, radius_)); PointLiesOnCircle(J, Circle(F, radius_)); "
}
] |
geometry3k/train/808/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)), 2x+4y); Equals(LengthOf(Line(A, D)), 21); Equals(LengthOf(Line(B, C)), 3x+3y); Equals(LengthOf(Line(A, B)), 6y+\\frac{1}{2}x); "
}
] |
geometry3k/train/809/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(N, P)), 8); Equals(LengthOf(Line(N, Q)), 12); Equals(LengthOf(Line(Q, P)), 20); Equals(LengthOf(Line(J, H)), 4x+7); Equals(LengthOf(Line(K, J)), 25); Equals(LengthOf(Line(K, H)), 6x-2); Equals(MeasureOf(Angle(P, Q, N)), MeasureOf(Angle(H, J, K))); Equals(MeasureOf(Angle(K, H, J)), MeasureOf(Angle(Q, N, P))); "
}
] |
geometry3k/train/810/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, Q)), 15); Equals(LengthOf(Line(Q, P)), 17); Equals(LengthOf(Line(R, P)), 8); Perpendicular(Line(R, Q), Line(R, P)); "
}
] |
geometry3k/train/811/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(X, P)), 8); Equals(LengthOf(Line(W, P)), 6); Equals(LengthOf(Line(Y, P)), 24); Equals(LengthOf(Line(Z, P)), 8); PointLiesOnLine(P, Line(Z, X)); PointLiesOnLine(P, Line(Y, W)); "
}
] |
geometry3k/train/812/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)), x); Equals(LengthOf(Line(B, C)), 24); Equals(MeasureOf(Angle(B, A, C)), 32); Perpendicular(Line(C, B), Line(A, C)); Perpendicular(Line(D, C), Line(D, A)); PointLiesOnLine(D, Line(A, B)); "
}
] |
geometry3k/train/815/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)), 3y-2); Equals(LengthOf(Line(A, D)), x+4); Equals(LengthOf(Line(C, B)), 2x-4); Equals(LengthOf(Line(A, C)), 4y-8); "
}
] |
geometry3k/train/818/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, E, A)), 148); Equals(MeasureOf(Angle(E, A, F)), 18); Equals(MeasureOf(Angle(Y, Z, X)), 5x-y); Equals(MeasureOf(Angle(Y, X, Z)), 3x+y); Equals(MeasureOf(Angle(X, Y, Z)), MeasureOf(A, E, F)); "
}
] |
geometry3k/train/820/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(E, Line(D, B)); PointLiesOnLine(E, Line(A, C)); PointLiesOnCircle(D, Circle(Z, radius_)); PointLiesOnCircle(B, Circle(Z, radius_)); PointLiesOnCircle(A, Circle(Z, radius_)); PointLiesOnCircle(C, Circle(Z, radius_)); "
}
] |
geometry3k/train/823/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(S, Q)), 33.2); Equals(LengthOf(Line(S, R)), 53); Equals(LengthOf(Line(R, Q)), 21); Equals(MeasureOf(Angle(S, R, Q)), x); "
}
] |
geometry3k/train/824/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(4)), MeasureOf(Angle(I, C, A))); Equals(MeasureOf(Angle(H, C, A)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(M, H, C)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(I, C, E))); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(F, H, G))); Equals(MeasureOf(Angle(F, C, E)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(D, H, I)), MeasureOf(Angle(7))); Equals(MeasureOf(Angle(8)), MeasureOf(Angle(D, H, F))); Parallel(Line(E, A), Line(M, D)); PointLiesOnLine(H, Line(M, D)); PointLiesOnLine(H, Line(C, F)); PointLiesOnLine(H, Line(F, I)); PointLiesOnLine(C, Line(A, E)); PointLiesOnLine(C, Line(I, H)); PointLiesOnLine(C, Line(F, I)); "
}
] |
geometry3k/train/826/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)), 12); Equals(LengthOf(Line(C, A)), z); Equals(LengthOf(Line(B, P)), 8); Equals(LengthOf(Line(P, A)), y); Equals(LengthOf(Line(B, A)), x); Perpendicular(Line(A, P), Line(C, P)); Perpendicular(Line(C, A), Line(A, B)); PointLiesOnLine(P, Line(B, C)); "
}
] |
geometry3k/train/830/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)), y); Equals(LengthOf(Line(C, B)), z); Equals(LengthOf(Line(C, D)), x); Equals(LengthOf(Line(A, D)), 9); Equals(LengthOf(Line(D, B)), 16); Perpendicular(Line(A, C), Line(B, C)); Perpendicular(Line(C, D), Line(D, A)); PointLiesOnLine(D, Line(B, A)); "
}
] |
geometry3k/train/831/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, A, B)), 50); Equals(MeasureOf(Angle(D, A, C)), x); PointLiesOnLine(A, Line(B, D)); "
}
] |
geometry3k/train/832/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(1)), MeasureOf(Angle(B, A, F))); Equals(MeasureOf(Angle(B, F, A)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(D, A, C))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(D, F, A))); Equals(MeasureOf(Angle(6)), MeasureOf(Angle(C, F, D))); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(A, D, F))); PointLiesOnLine(F, Line(B, D)); PointLiesOnLine(F, Line(A, C)); "
}
] |
geometry3k/train/833/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)), x); Equals(LengthOf(Line(B, C)), 48); Equals(LengthOf(Line(A, C)), 14); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/837/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, E, K)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(A, L, E)), 133); Equals(MeasureOf(Angle(G, K, I)), 126); PointLiesOnLine(L, Line(B, A)); PointLiesOnLine(E, Line(L, C)); PointLiesOnLine(J, Line(C, L)); PointLiesOnLine(J, Line(L, E)); PointLiesOnLine(E, Line(C, D)); PointLiesOnLine(J, Line(D, C)); PointLiesOnLine(L, Line(C, D)); PointLiesOnLine(E, Line(J, C)); PointLiesOnLine(J, Line(E, D)); PointLiesOnLine(L, Line(D, E)); PointLiesOnLine(L, Line(D, J)); PointLiesOnLine(K, Line(H, E)); PointLiesOnLine(K, Line(J, I)); PointLiesOnLine(E, Line(H, G)); PointLiesOnLine(K, Line(G, H)); PointLiesOnLine(E, Line(G, K)); PointLiesOnLine(J, Line(K, F)); PointLiesOnLine(J, Line(I, F)); PointLiesOnLine(K, Line(I, F)); "
}
] |
geometry3k/train/838/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, D)), x); Equals(LengthOf(Line(D, C)), 6); Equals(LengthOf(Line(D, E)), 3); Equals(LengthOf(Line(A, D)), 9); PointLiesOnLine(D, Line(A, B)); PointLiesOnLine(D, Line(C, E)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(B, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(E, Circle(F, radius_)); "
}
] |
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