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stringlengths 34
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geometry3k/train/522/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, P)), 2x); Equals(LengthOf(Line(R, Q)), 3y+8); Equals(LengthOf(Line(S, R)), 2y); Equals(LengthOf(Line(S, P)), x); Perpendicular(Line(S, R), Line(Q, S)); PointLiesOnLine(S, Line(R, P)); "
}
] |
geometry3k/train/524/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, R)), 5); Equals(LengthOf(Line(S, J)), 5); Perpendicular(Line(R, J), Line(R, H)); Perpendicular(Line(J, S), Line(S, L)); PointLiesOnLine(R, Line(H, G)); PointLiesOnLine(S, Line(L, K)); PointLiesOnCircle(G, Circle(J, radius_)); PointLiesOnCircle(H, Circle(J, radius_)); PointLiesOnCircle(L, Circle(J, radius_)); PointLiesOnCircle(K, Circle(J, radius_)); "
}
] |
geometry3k/train/526/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-5); Equals(LengthOf(Line(B, C)), 54); Equals(LengthOf(Line(B, A)), x); Equals(LengthOf(Line(B, D)), 28); Equals(MeasureOf(Angle(D, A, C)), MeasureOf(Angle(B, A, D))); PointLiesOnLine(D, Line(B, C)); "
}
] |
geometry3k/train/527/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, D, F)), 3x+2); Equals(MeasureOf(Angle(A, F, G)), 2x); Equals(MeasureOf(Angle(B, I, D)), x+5); Equals(MeasureOf(Angle(B, G, C)), 2x+1); PointLiesOnLine(F, Line(D, A)); PointLiesOnLine(G, Line(C, F)); PointLiesOnLine(I, Line(B, G)); PointLiesOnLine(D, Line(H, I)); "
}
] |
geometry3k/train/529/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)), 16); Equals(LengthOf(Line(A, D)), 8); Equals(MeasureOf(Angle(D, B, A)), y); Equals(LengthOf(Line(B, D)), x); Perpendicular(Line(B, D), Line(D, A)); "
}
] |
geometry3k/train/530/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, B)), 14); Equals(LengthOf(Line(F, A)), LengthOf(Line(A, E))); PointLiesOnLine(A, Line(F, E)); PointLiesOnCircle(B, Circle(A, radius_)); PointLiesOnCircle(H, Circle(A, radius_)); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(H, Circle(E, radius_)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(B, Circle(F, radius_)); "
}
] |
geometry3k/train/531/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)), 8); Equals(LengthOf(Line(A, C)), x); Equals(LengthOf(Line(D, B)), 16); Equals(LengthOf(Line(B, C)), z); Equals(LengthOf(Line(B, A)), y); Perpendicular(Line(D, A), Line(B, D)); Perpendicular(Line(D, B), Line(A, B)); PointLiesOnLine(D, Line(C, A)); "
}
] |
geometry3k/train/533/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": ""
}
] |
geometry3k/train/535/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(D, Line(A, C)); "
}
] |
geometry3k/train/536/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, A)), x); Equals(LengthOf(Line(B, C)), z); Equals(LengthOf(Line(B, A)), 20); Equals(LengthOf(Line(A, D)), 10); Equals(LengthOf(Line(D, B)), y); Perpendicular(Line(A, B), Line(A, C)); Perpendicular(Line(B, D), Line(C, B)); PointLiesOnLine(A, Line(D, C)); "
}
] |
geometry3k/train/537/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, C)), 46); Equals(LengthOf(Line(E, H)), 38); PointLiesOnLine(E, Line(F, D)); PointLiesOnLine(H, Line(G, C)); "
}
] |
geometry3k/train/540/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)), 8); Equals(LengthOf(Line(S, J)), 10); Equals(MeasureOf(Angle(K, L, S)), 24.5); Equals(MeasureOf(Angle(K, P, L)), 28); Perpendicular(Line(K, J), Line(K, S)); Perpendicular(Line(P, Q), Line(S, Q)); Perpendicular(Line(M, S), Line(P, M)); PointLiesOnLine(K, Line(J, L)); PointLiesOnLine(M, Line(L, P)); PointLiesOnLine(S, Line(L, Q)); PointLiesOnLine(Q, Line(J, P)); PointLiesOnLine(S, Line(J, M)); PointLiesOnLine(S, Line(P, K)); "
}
] |
geometry3k/train/541/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, R)), 18); Equals(LengthOf(Line(W, T)), 12); Equals(MeasureOf(Angle(V, W, T)), 60); Perpendicular(Line(A, T), Line(W, V)); PointLiesOnLine(A, Line(V, W)); "
}
] |
geometry3k/train/542/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)), 17); Equals(LengthOf(Line(F, G)), 9x-6); Equals(LengthOf(Line(H, G)), 7x+4); Equals(LengthOf(Line(F, G)), LengthOf(Line(H, G))); "
}
] |
geometry3k/train/543/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(LengthOf(Line(A, B)), 6\\sqrt{3}); Equals(MeasureOf(Angle(B, C, A)), 60); Equals(LengthOf(Line(C, A)), x); Perpendicular(Line(B, A), Line(C, A)); "
}
] |
geometry3k/train/544/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)), x+2); Equals(LengthOf(Line(C, B)), 8); Equals(LengthOf(Line(C, D)), y-3); Equals(LengthOf(Line(G, H)), 5); Equals(LengthOf(Line(F, E)), 15); Equals(LengthOf(Line(H, E)), 10); Equals(MeasureOf(Angle(D, A, B)), MeasureOf(Angle(E, F, G))); Equals(MeasureOf(Angle(C, B, A)), MeasureOf(Angle(F, E, H))); Equals(MeasureOf(Angle(B, C, D)), MeasureOf(Angle(E, H, G))); Equals(MeasureOf(Angle(H, G, F)), MeasureOf(Angle(C, D, A))); "
}
] |
geometry3k/train/545/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, C)), x-11); Equals(MeasureOf(Angle(E, B, A)), x+10); Equals(MeasureOf(Angle(B, D, G)), 31); Equals(MeasureOf(Angle(H, C, G)), 2x-42); PointLiesOnLine(C, Line(A, H)); PointLiesOnLine(A, Line(F, B)); PointLiesOnLine(B, Line(D, E)); PointLiesOnLine(D, Line(C, G)); "
}
] |
geometry3k/train/550/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(U, S)); PointLiesOnCircle(V, Circle(R, radius_)); PointLiesOnCircle(U, Circle(R, radius_)); PointLiesOnCircle(T, Circle(R, radius_)); PointLiesOnCircle(S, Circle(R, radius_)); "
}
] |
geometry3k/train/551/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, L)), 164); Equals(LengthOf(Line(K, J)), 15); PointLiesOnCircle(J, Circle(K, radius_)); PointLiesOnCircle(L, Circle(K, radius_)); "
}
] |
geometry3k/train/552/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, J, M)), MeasureOf(Angle(S, Q, T))); Equals(MeasureOf(Angle(L, M, J)), MeasureOf(Angle(Q, T, S))); Equals(LengthOf(Line(M, J)), 4); Equals(LengthOf(Line(T, S)), 3); Equals(LengthOf(Line(T, Q)), 2); Equals(LengthOf(Line(S, Q)), 5); Equals(LengthOf(Line(M, L)), 6x-3); Equals(LengthOf(Line(J, L)), 3y-2); "
}
] |
geometry3k/train/553/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)), 20); Equals(LengthOf(Line(B, C)), y); Equals(MeasureOf(Angle(C, A, B)), 60); Equals(LengthOf(Line(C, A)), x); Perpendicular(Line(C, A), Line(C, B)); "
}
] |
geometry3k/train/554/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, K)), 20); Equals(LengthOf(Line(L, K)), z); Equals(LengthOf(Line(L, M)), x); Equals(LengthOf(Line(J, M)), 5); Equals(LengthOf(Line(J, L)), y); Perpendicular(Line(L, M), Line(M, K)); Perpendicular(Line(L, J), Line(K, L)); PointLiesOnLine(M, Line(K, J)); "
}
] |
geometry3k/train/555/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)), 28); Equals(LengthOf(Line(A, C)), 20); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/557/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, P)), 10); PointLiesOnLine(R, Line(M, Q)); PointLiesOnLine(R, Line(L, P)); "
}
] |
geometry3k/train/560/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, R)), 6x-5); Equals(LengthOf(Line(R, Q)), 5x); Equals(LengthOf(Line(Q, S)), 3x+10); Equals(LengthOf(Line(R, S)), LengthOf(Line(Q, R))); Equals(LengthOf(Line(S, Q)), LengthOf(Line(Q, R))); "
}
] |
geometry3k/train/562/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)), 6); Equals(LengthOf(Line(A, C)), 8); Equals(LengthOf(Line(S, A)), z); Equals(LengthOf(Line(S, B)), x); Perpendicular(Line(C, S), Line(A, C)); Perpendicular(Line(S, A), Line(B, A)); PointLiesOnLine(C, Line(S, B)); "
}
] |
geometry3k/train/563/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(W, W')), x); Equals(LengthOf(Line(W', F)), 10.5); Equals(LengthOf(Line(W, F)), 14); PointLiesOnLine(C, Line(A, F)); PointLiesOnLine(X, Line(F, W)); "
}
] |
geometry3k/train/564/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(H, J, P)), 57); Equals(MeasureOf(Angle(J, H, L)), x); PointLiesOnLine(J, Line(K, L)); PointLiesOnLine(P, Line(K, M)); PointLiesOnLine(H, Line(L, M)); "
}
] |
geometry3k/train/565/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, F)), x); Equals(LengthOf(Line(D, B)), 3); Equals(LengthOf(Line(C, F)), 5); Equals(LengthOf(Line(D, A)), 9); PointLiesOnLine(D, Line(B, A)); PointLiesOnLine(E, Line(B, A)); PointLiesOnLine(E, Line(D, A)); PointLiesOnLine(F, Line(C, B)); PointLiesOnLine(D, Line(E, B)); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); "
}
] |
geometry3k/train/566/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(7)), MeasureOf(Angle(P, M, K))); Equals(MeasureOf(Angle(H, M, K)), MeasureOf(Angle(5))); Equals(MeasureOf(Angle(8)), MeasureOf(Angle(P, M, D))); Equals(MeasureOf(Angle(G, H, M)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(H, M, D)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(G, H, E)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(F, H, M))); Equals(MeasureOf(Angle(F, H, E)), MeasureOf(Angle(2))); Parallel(Line(G, F), Line(K, D)); PointLiesOnLine(H, Line(M, E)); PointLiesOnLine(H, Line(E, P)); PointLiesOnLine(H, Line(G, F)); PointLiesOnLine(M, Line(L, E)); PointLiesOnLine(M, Line(P, E)); PointLiesOnLine(M, Line(K, D)); "
}
] |
geometry3k/train/568/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, J, H)), x); Equals(MeasureOf(Angle(M, H, P)), 44); Equals(MeasureOf(Angle(J, H, L)), 76); PointLiesOnLine(J, Line(K, L)); PointLiesOnLine(P, Line(K, M)); PointLiesOnLine(H, Line(M, L)); "
}
] |
geometry3k/train/569/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)), 14); Equals(LengthOf(Line(A, M)), 9); Equals(LengthOf(Line(M, E)), 15); PointLiesOnLine(A, Line(B, M)); PointLiesOnLine(G, Line(B, C)); PointLiesOnLine(F, Line(D, M)); PointLiesOnCircle(A, Circle(H, radius_)); PointLiesOnCircle(F, Circle(H, radius_)); PointLiesOnCircle(L, Circle(H, radius_)); "
}
] |
geometry3k/train/572/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(L, G)), 3); Equals(LengthOf(Line(E, L)), 4); Equals(LengthOf(Line(G, O)), x); Equals(LengthOf(Line(E, S)), 9); PointLiesOnLine(G, Line(L, O)); PointLiesOnCircle(E, Circle(B, radius_)); PointLiesOnCircle(O, Circle(B, radius_)); PointLiesOnCircle(S, Circle(B, radius_)); PointLiesOnCircle(G, Circle(B, radius_)); "
}
] |
geometry3k/train/573/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)), x+15); Equals(LengthOf(Line(B, C)), 2x-5); PointLiesOnCircle(B, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); PointLiesOnCircle(A, Circle(D, radius_)); "
}
] |
geometry3k/train/574/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, H)), 6x+1); Equals(LengthOf(Line(G, F)), 3x+10); Equals(LengthOf(Line(G, H)), 9x-8); "
}
] |
geometry3k/train/575/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, J, K)), 3y+9); Equals(MeasureOf(Angle(G, K, J)), x+21); Equals(MeasureOf(Angle(J, H, G)), 2x); Equals(MeasureOf(Angle(H, G, K)), 4y-11); PointLiesOnCircle(G, Circle(O, radius_)); PointLiesOnCircle(K, Circle(O, radius_)); PointLiesOnCircle(J, Circle(O, radius_)); PointLiesOnCircle(H, Circle(O, radius_)); "
}
] |
geometry3k/train/576/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, H)); PointLiesOnCircle(U, Circle(M, radius_)); PointLiesOnCircle(A, Circle(M, radius_)); PointLiesOnCircle(S, Circle(M, radius_)); PointLiesOnCircle(R, Circle(M, radius_)); PointLiesOnCircle(D, Circle(M, radius_)); PointLiesOnCircle(H, Circle(M, radius_)); "
}
] |
geometry3k/train/577/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, K, H)), 122); PointLiesOnLine(K, Line(G, J)); PointLiesOnCircle(L, Circle(K, radius_)); PointLiesOnCircle(H, Circle(K, radius_)); PointLiesOnCircle(J, Circle(K, radius_)); PointLiesOnCircle(G, Circle(K, radius_)); "
}
] |
geometry3k/train/579/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(N, S)), 9); PointLiesOnCircle(P, Circle(J, radius_)); PointLiesOnCircle(S, Circle(J, radius_)); PointLiesOnCircle(B, Circle(J, radius_)); PointLiesOnCircle(N, Circle(J, radius_)); "
}
] |
geometry3k/train/580/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, A)), 12); Equals(LengthOf(Line(D, C)), 9); Equals(LengthOf(Line(F, D)), x); Equals(LengthOf(Line(Y, Z)), 10); Equals(LengthOf(Line(V, Z)), 3y-1); Equals(LengthOf(Line(W, Y)), 6); "
}
] |
geometry3k/train/583/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, C, D)), x+25); Equals(MeasureOf(Angle(C, D, E)), 2x-22); Equals(MeasureOf(Angle(C, B, A)), 1.5x+3); Equals(MeasureOf(Angle(B, A, E)), x+27); Equals(MeasureOf(Angle(A, E, D)), x); "
}
] |
geometry3k/train/585/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(S, X)), x+2); Equals(LengthOf(Line(S, Z)), x+6); Equals(LengthOf(Line(Y, S)), x+12); Equals(LengthOf(Line(W, S)), x); PointLiesOnLine(S, Line(W, Y)); PointLiesOnLine(S, Line(X, Z)); PointLiesOnCircle(W, Circle(B, radius_)); PointLiesOnCircle(Y, Circle(B, radius_)); PointLiesOnCircle(X, Circle(B, radius_)); PointLiesOnCircle(Z, Circle(B, radius_)); "
}
] |
geometry3k/train/586/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(A, B)), 15); Equals(MeasureOf(Angle(C, B, A)), 30); Equals(LengthOf(Line(B, C)), x); Perpendicular(Line(A, C), Line(C, B)); "
}
] |
geometry3k/train/588/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, R)), 5x-9); Equals(LengthOf(Line(T, V)), 2x+3); Equals(LengthOf(Arc(R, S)), LengthOf(Arc(V, T))); PointLiesOnCircle(S, Circle(W, radius_)); PointLiesOnCircle(T, Circle(W, radius_)); PointLiesOnCircle(R, Circle(W, radius_)); PointLiesOnCircle(V, Circle(W, radius_)); "
}
] |
geometry3k/train/589/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, M, L)), 2x-8); Equals(MeasureOf(Angle(M, J, K)), 3x-6); Equals(MeasureOf(Angle(J, K, L)), x+10); Equals(MeasureOf(Angle(K, L, M)), x); "
}
] |
geometry3k/train/590/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, G, B)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(F, G, B)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(A, G, R))); Equals(MeasureOf(Angle(8)), MeasureOf(Angle(A, G, F))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(S, A, B))); Equals(MeasureOf(Angle(7)), MeasureOf(Angle(B, A, D))); Equals(MeasureOf(Angle(H, A, S)), MeasureOf(Angle(5))); Equals(MeasureOf(Angle(D, A, H)), MeasureOf(Angle(6))); Parallel(Line(F, R), Line(D, S)); PointLiesOnLine(G, Line(R, F)); PointLiesOnLine(A, Line(H, G)); PointLiesOnLine(G, Line(A, B)); PointLiesOnLine(A, Line(H, B)); PointLiesOnLine(G, Line(B, H)); PointLiesOnLine(A, Line(D, S)); "
}
] |
geometry3k/train/591/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\\sqrt{2}); Equals(LengthOf(Line(A, B)), LengthOf(Line(B, C))); PointLiesOnLine(D, Line(A, C)); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(B, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); "
}
] |
geometry3k/train/592/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)), 20); Equals(LengthOf(Line(D, E)), 30); Equals(LengthOf(Line(E, C)), 20); Equals(LengthOf(Line(A, E)), 30); Perpendicular(Line(B, E), Line(E, A)); PointLiesOnLine(E, Line(D, A)); PointLiesOnLine(E, Line(B, C)); "
}
] |
geometry3k/train/593/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, A)), 120); Equals(MeasureOf(Angle(D, B, E)), MeasureOf(Angle(3))); Equals(MeasureOf(Arc(D, E)), 100); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(B, Line(E, A)); PointLiesOnLine(F, Line(E, A)); PointLiesOnLine(B, Line(F, E)); PointLiesOnLine(B, Line(D, C)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(D, Circle(F, radius_)); PointLiesOnCircle(E, Circle(F, radius_)); "
}
] |
geometry3k/train/595/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(O, A), Line(O, C)); PointLiesOnLine(O, Line(E, C)); PointLiesOnLine(O, Line(A, B)); PointLiesOnCircle(E, Circle(O, radius_)); PointLiesOnCircle(F, Circle(O, radius_)); PointLiesOnCircle(A, Circle(O, radius_)); PointLiesOnCircle(C, Circle(O, radius_)); PointLiesOnCircle(D, Circle(O, radius_)); PointLiesOnCircle(B, Circle(O, radius_)); "
}
] |
geometry3k/train/596/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, C)), 5); Equals(LengthOf(Line(T, C)), 12); Equals(MeasureOf(Angle(C, T, Q)), 120); Equals(MeasureOf(Angle(R, B, A)), 45); PointLiesOnLine(A, Line(T, Q)); PointLiesOnLine(B, Line(C, R)); "
}
] |
geometry3k/train/597/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)), 5); Equals(LengthOf(Line(A, D)), 8); Equals(LengthOf(Line(D, F)), 6); PointLiesOnLine(D, Line(A, F)); PointLiesOnLine(D, Line(B, E)); PointLiesOnCircle(A, Circle(C, radius_)); PointLiesOnCircle(B, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); PointLiesOnCircle(F, Circle(C, radius_)); "
}
] |
geometry3k/train/598/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, E, D)), 45); Equals(LengthOf(Line(A, G)), x); Equals(LengthOf(Line(A, E)), 8); Equals(LengthOf(Line(G, D)), y); Equals(MeasureOf(Angle(A, D, E)), 30); Perpendicular(Line(A, G), Line(G, D)); PointLiesOnLine(G, Line(E, D)); "
}
] |
geometry3k/train/603/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, F)), 4.2); Equals(LengthOf(Line(D, B)), 5.4); Perpendicular(Line(E, B), Line(D, B)); Equals(LengthOf(Line(B, E)), LengthOf(Line(F, D))); Equals(LengthOf(Line(F, E)), LengthOf(Line(B, D))); "
}
] |
geometry3k/train/605/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, D, A)), x); Equals(LengthOf(Line(A, C)), 24); Equals(LengthOf(Line(D, A)), 36); Equals(MeasureOf(Angle(B, A, C)), y); Perpendicular(Line(C, A), Line(C, B)); Equals(LengthOf(Line(C, B)), LengthOf(Line(B, D))); PointLiesOnLine(B, Line(C, D)); "
}
] |
geometry3k/train/608/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, E)), 5x+62); Equals(MeasureOf(Angle(C, B, D)), 37); Equals(MeasureOf(Angle(B, D, C)), 3x+47); PointLiesOnLine(C, Line(D, E)); "
}
] |
geometry3k/train/611/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)), 6); Equals(MeasureOf(Angle(E, D, A)), x); Equals(MeasureOf(Angle(B, D, C)), x); PointLiesOnLine(D, Line(C, E)); "
}
] |
geometry3k/train/612/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)), 3y-8); Equals(MeasureOf(Angle(F, B, A)), 20); Equals(LengthOf(Line(D, A)), 13); Equals(LengthOf(Line(B, C)), 2x+7); Equals(MeasureOf(Angle(C, F, B)), 49); Equals(MeasureOf(Angle(F, D, A)), 59); Equals(LengthOf(Line(D, C)), 10); PointLiesOnLine(F, Line(B, D)); PointLiesOnLine(F, Line(C, A)); "
}
] |
geometry3k/train/613/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(MeasureOf(Angle(B, C, D)), x); Equals(LengthOf(Line(A, B)), 9.6); Perpendicular(Line(B, D), Line(D, C)); Equals(LengthOf(Line(A, C)), LengthOf(Line(D, C))); Equals(LengthOf(Line(C, D)), LengthOf(Line(B, D))); Equals(LengthOf(Line(A, B)), LengthOf(Line(C, D))); "
}
] |
geometry3k/train/614/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)), 7); Equals(LengthOf(Line(A, B)), x); Equals(MeasureOf(Angle(B, C, A)), 18); Equals(LengthOf(Line(B, C)), 14.7); "
}
] |
geometry3k/train/616/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)), 4x+9); Equals(MeasureOf(Angle(A, D, C)), 7x-6); Equals(LengthOf(Line(C, D)), 7x-6); PointLiesOnLine(D, Line(B, C)); "
}
] |
geometry3k/train/617/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, F, G)), x+20); Equals(MeasureOf(Angle(F, E, J)), x); Equals(MeasureOf(Angle(J, H, G)), x-5); Equals(MeasureOf(Angle(E, J, H)), x+10); Equals(MeasureOf(Angle(F, G, H)), x+5); "
}
] |
geometry3k/train/618/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, C), Line(E, B)); PointLiesOnLine(B, Line(A, C)); PointLiesOnLine(E, Line(A, D)); "
}
] |
geometry3k/train/619/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, B)), 72); Equals(LengthOf(Line(A, C)), 78); Perpendicular(Line(B, C), Line(A, B)); "
}
] |
geometry3k/train/622/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(X, S), Line(R, S)); PointLiesOnLine(S, Line(X, Y)); PointLiesOnLine(R, Line(X, Z)); PointLiesOnLine(R, Line(Y, W)); PointLiesOnCircle(X, Circle(R, radius_)); PointLiesOnCircle(Y, Circle(R, radius_)); PointLiesOnCircle(W, Circle(R, radius_)); PointLiesOnCircle(Z, Circle(R, radius_)); "
}
] |
geometry3k/train/623/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)), 2x+4); Equals(LengthOf(Line(C, A)), 3x-1); Equals(LengthOf(Line(B, C)), 4x-8); "
}
] |
geometry3k/train/624/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(E, A, B))); Equals(MeasureOf(Angle(E, B, A)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(D, B, E))); Equals(MeasureOf(Angle(6)), MeasureOf(Angle(A, E, B))); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(B, E, C))); Equals(MeasureOf(Angle(B, C, E)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(D, E, C)), MeasureOf(Angle(7))); Equals(MeasureOf(Angle(D, C, E)), MeasureOf(Angle(8))); Equals(MeasureOf(Angle(9)), MeasureOf(Angle(E, D, B))); Parallel(Line(E, C), Line(B, A)); PointLiesOnLine(C, Line(B, D)); PointLiesOnLine(E, Line(D, A)); "
}
] |
geometry3k/train/625/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(R, P, S)), 130); Equals(MeasureOf(Angle(T, P, Q)), 112); PointLiesOnLine(P, Line(T, R)); PointLiesOnCircle(S, Circle(P, radius_)); PointLiesOnCircle(T, Circle(P, radius_)); PointLiesOnCircle(R, Circle(P, radius_)); PointLiesOnCircle(Q, Circle(P, radius_)); "
}
] |
geometry3k/train/627/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, Y)), 105); Equals(MeasureOf(Angle(Z, Y, X)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(Z, W, X)), 23); Equals(MeasureOf(Angle(W, Z, X)), 24); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(Y, Z, X))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(Z, X, W))); Equals(MeasureOf(Angle(X, Y, Z)), MeasureOf(Angle(Y, Z, X))); "
}
] |
geometry3k/train/628/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(A, E), Line(E, D)); PointLiesOnLine(E, Line(B, A)); PointLiesOnLine(E, Line(C, D)); PointLiesOnCircle(B, Circle(A, radius_)); PointLiesOnCircle(C, Circle(A, radius_)); PointLiesOnCircle(D, Circle(A, radius_)); "
}
] |
geometry3k/train/630/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)), x); Equals(MeasureOf(Angle(A, C, B)), 86); Equals(MeasureOf(Angle(B, A, C)), 33); Equals(LengthOf(Line(A, C)), 24); "
}
] |
geometry3k/train/632/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)), 11.2); Equals(LengthOf(Line(B, C)), 12.4); Equals(MeasureOf(Angle(C, B, A)), 67); "
}
] |
geometry3k/train/633/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)), 82); Equals(MeasureOf(Angle(R, P, Q)), 97); Equals(MeasureOf(Angle(P, R, S)), 3y-13); Equals(MeasureOf(Angle(A, D, C)), x+34); Equals(MeasureOf(Angle(R, S, Q)), 98); Equals(MeasureOf(Angle(D, C, B)), 83); "
}
] |
geometry3k/train/634/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, A)), 2x); Equals(LengthOf(Line(R, A)), x+9); Equals(LengthOf(Line(R, T)), 3x-9); "
}
] |
geometry3k/train/636/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(W, X), Line(W, Z)); PointLiesOnLine(P, Line(W, Y)); PointLiesOnLine(P, Line(Z, X)); "
}
] |
geometry3k/train/637/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)), 9x-1); Equals(LengthOf(Line(C, A)), 4x+1); Equals(LengthOf(Line(C, B)), 5x-0.5); Equals(LengthOf(Line(C, A)), LengthOf(Line(B, C))); "
}
] |
geometry3k/train/638/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(Z, X)), 14); Equals(LengthOf(Line(X, Y)), 7); Equals(LengthOf(Line(Z, Y)), x); Perpendicular(Line(X, Y), Line(Z, Y)); "
}
] |
geometry3k/train/639/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(P, S, R)), 15x+42); Equals(LengthOf(Line(R, Q)), 5); Equals(LengthOf(Angle(Q, S)), 10x-7); Equals(LengthOf(Line(R, S)), 5x+3); Equals(LengthOf(Line(Q, S)), LengthOf(Line(S, R))); PointLiesOnLine(A, Line(Q, R)); "
}
] |
geometry3k/train/640/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(T, V), Line(V, X)); PointLiesOnLine(V, Line(T, Z)); PointLiesOnLine(V, Line(X, Y)); PointLiesOnLine(T, Line(V, W)); PointLiesOnLine(V, Line(W, Z)); PointLiesOnLine(T, Line(Z, W)); PointLiesOnCircle(X, Circle(T, radius_)); PointLiesOnCircle(V, Circle(T, radius_)); PointLiesOnCircle(W, Circle(T, radius_)); PointLiesOnCircle(Y, Circle(T, radius_)); "
}
] |
geometry3k/train/641/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, D)), 25); Equals(MeasureOf(Angle(E, C, B)), x); Equals(MeasureOf(Angle(B, D, C)), 20); PointLiesOnLine(C, Line(D, E)); "
}
] |
geometry3k/train/642/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)), 15); Equals(LengthOf(Line(B, D)), y); Equals(LengthOf(Line(A, C)), 19); Equals(LengthOf(Line(B, A)), x); Equals(LengthOf(Line(C, B)), z); Perpendicular(Line(C, A), Line(A, B)); Perpendicular(Line(B, D), Line(B, C)); PointLiesOnLine(A, Line(D, C)); "
}
] |
geometry3k/train/643/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(Q, N)); PointLiesOnLine(A, Line(M, P)); "
}
] |
geometry3k/train/646/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, H, B)), \\frac{1}{4}x); Equals(MeasureOf(Angle(H, D, B)), 4x-8); Equals(MeasureOf(Angle(B, C, H)), 8y-12); Equals(MeasureOf(Angle(C, B, H)), y-8); "
}
] |
geometry3k/train/647/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, A, B)), 78); Equals(LengthOf(Line(C, A)), x); Equals(MeasureOf(Angle(A, B, C)), 60); Equals(LengthOf(Line(C, B)), 8); "
}
] |
geometry3k/train/649/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)), 30); Equals(LengthOf(Line(D, B)), x); Equals(MeasureOf(Angle(B, C, A)), 42); Perpendicular(Line(A, D), Line(B, D)); Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C))); PointLiesOnLine(D, Line(C, A)); "
}
] |
geometry3k/train/650/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(A, C)), 133); Equals(MeasureOf(Arc(B, E)), 133); Equals(LengthOf(Line(A, C)), 4x-2); Equals(LengthOf(Line(B, E)), 6x-10); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(B, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); PointLiesOnCircle(E, Circle(D, radius_)); "
}
] |
geometry3k/train/653/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, G)), 3x-2); Equals(LengthOf(Line(A, B)), 13); Equals(LengthOf(Line(F, H)), 11); Equals(LengthOf(Line(C, B)), 7); Equals(LengthOf(Line(A, C)), 2x+5); Equals(LengthOf(Line(F, G)), 4x+1); "
}
] |
geometry3k/train/656/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, X)), 5); Equals(LengthOf(Line(Y, W)), 8); PointLiesOnLine(A, Line(Y, W)); PointLiesOnLine(A, Line(X, Z)); "
}
] |
geometry3k/train/657/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(A, B, C)), 24); Equals(LengthOf(Line(A, B)), 19); Perpendicular(Line(A, C), Line(A, B)); "
}
] |
geometry3k/train/658/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, G)), x); Equals(LengthOf(Line(V, G)), 12); Equals(LengthOf(Line(B, M)), 16); Equals(LengthOf(Line(M, H)), 22); Equals(MeasureOf(Angle(B, M, H)), MeasureOf(Angle(V, G, C))); Equals(MeasureOf(Angle(H, B, M)), MeasureOf(Angle(C, V, G))); "
}
] |
geometry3k/train/659/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-4); Equals(LengthOf(Line(A, B)), x); Equals(LengthOf(Line(B, C)), 8); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/660/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, B)), 6x); Equals(MeasureOf(Angle(C, A, F)), 139); Equals(MeasureOf(Angle(D, B, G)), 9x); Equals(MeasureOf(Angle(E, D, A)), 2x); PointLiesOnLine(C, Line(H, A)); PointLiesOnLine(B, Line(G, C)); PointLiesOnLine(A, Line(F, D)); PointLiesOnLine(A, Line(F, G)); PointLiesOnLine(D, Line(B, E)); "
}
] |
geometry3k/train/661/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(O, N)), 6); Equals(LengthOf(Line(P, N)), x); Equals(LengthOf(Line(P, O)), 10); PointLiesOnLine(A, Line(P, O)); PointLiesOnCircle(N, Circle(O, radius_)); PointLiesOnCircle(A, Circle(O, radius_)); "
}
] |
geometry3k/train/663/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)), 13); Equals(LengthOf(Line(B, C)), 5); Equals(MeasureOf(Angle(B, A, C)), x); Equals(LengthOf(Line(A, C)), 12); "
}
] |
geometry3k/train/664/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)), 4x+3); Equals(LengthOf(Line(K, J)), 6x-5); Equals(LengthOf(Line(M, P)), 3y+8); Equals(LengthOf(Line(P, Q)), 5y-7); Equals(LengthOf(Line(P, M)), LengthOf(Line(Q, P))); Parallel(Line(P, K), Line(M, J)); Parallel(Line(Q, L), Line(K, P)); PointLiesOnLine(P, Line(M, Q)); PointLiesOnLine(K, Line(J, L)); "
}
] |
geometry3k/train/665/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, D, A)), 7y-4); Equals(MeasureOf(Angle(A, D, B)), 11x-1); Equals(MeasureOf(Angle(H, F, D)), 7x+9); Equals(MeasureOf(Angle(H, F, C)), z); Equals(MeasureOf(Angle(D, A, G)), 2y+5); Parallel(Line(G, A), Line(D, B)); Parallel(Line(B, D), Line(H, F)); PointLiesOnLine(F, Line(C, D)); PointLiesOnLine(A, Line(D, E)); "
}
] |
geometry3k/train/666/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, L)), 4x); Equals(LengthOf(Line(J, K)), 3x+6); Equals(LengthOf(Line(L, J)), 5x-6); Equals(LengthOf(Line(K, L)), LengthOf(Line(J, K))); Equals(LengthOf(Line(K, L)), LengthOf(Line(L, J))); "
}
] |
geometry3k/train/668/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(Y, Line(C, I)); PointLiesOnLine(W, Line(C, I)); PointLiesOnLine(X, Line(I, C)); PointLiesOnLine(W, Line(Y, I)); PointLiesOnLine(X, Line(Y, I)); PointLiesOnLine(Y, Line(Z, I)); PointLiesOnLine(W, Line(I, Z)); PointLiesOnLine(X, Line(I, Z)); PointLiesOnLine(W, Line(I, X)); PointLiesOnLine(Y, Line(W, C)); PointLiesOnLine(X, Line(C, W)); PointLiesOnLine(Y, Line(X, C)); PointLiesOnLine(X, Line(Y, W)); PointLiesOnLine(Y, Line(Z, W)); PointLiesOnLine(X, Line(Z, W)); PointLiesOnLine(Y, Line(X, Z)); PointLiesOnCircle(I, Circle(W, radius_)); PointLiesOnCircle(Y, Circle(W, radius_)); PointLiesOnCircle(C, Circle(Z, radius_)); PointLiesOnCircle(X, Circle(Z, radius_)); "
}
] |
geometry3k/train/669/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)), x); Equals(LengthOf(Line(D, E)), 9); Equals(LengthOf(Line(E, A)), 3); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(B, Line(A, D)); PointLiesOnLine(E, Line(D, A)); PointLiesOnLine(B, Line(E, D)); PointLiesOnCircle(D, Circle(B, radius_)); PointLiesOnCircle(E, Circle(B, radius_)); PointLiesOnCircle(F, Circle(B, radius_)); "
}
] |
geometry3k/train/670/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(W, T)), 14.8); Equals(LengthOf(Line(Z, Y)), 8); Equals(LengthOf(Line(R, V)), x); PointLiesOnLine(Z, Line(W, R)); PointLiesOnLine(Y, Line(T, V)); "
}
] |
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