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stringlengths 34
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geometry3k/train/1025/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)), 4x); Equals(LengthOf(Line(R, S)), 2x+1); Equals(LengthOf(Line(S, Q)), 6x-1); "
}
] |
geometry3k/train/1026/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, N)), 2\\sqrt{2}); Equals(LengthOf(Line(C, B)), LengthOf(Line(N, B))); Equals(LengthOf(Line(B, N)), LengthOf(Line(E, N))); Equals(LengthOf(Line(E, C)), LengthOf(Line(E, N))); "
}
] |
geometry3k/train/1028/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)), 3x+2); Equals(LengthOf(Line(T, R)), 2x+4); Equals(LengthOf(Line(S, R)), LengthOf(Line(R, T))); "
}
] |
geometry3k/train/1029/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(MeasureOf(Angle(C, B, A)), 29); Equals(MeasureOf(Angle(A, C, B)), 73); Equals(LengthOf(Line(A, C)), x); "
}
] |
geometry3k/train/1030/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, X)), 120); Perpendicular(Line(W, X), Line(Z, W)); "
}
] |
geometry3k/train/1031/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)), 120); Equals(MeasureOf(Angle(C, D, A)), 85); Equals(LengthOf(Line(C, B)), LengthOf(Line(C, D))); Equals(LengthOf(Line(B, A)), LengthOf(Line(A, D))); "
}
] |
geometry3k/train/1032/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, L)), 12); Perpendicular(Line(K, J), Line(K, M)); Equals(LengthOf(Line(J, M)), LengthOf(Line(L, M))); PointLiesOnLine(K, Line(J, L)); "
}
] |
geometry3k/train/1035/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, O, C)), 2x+41); Equals(MeasureOf(Angle(E, D, C)), 115); Equals(LengthOf(Line(D, C)), 3y+13); Equals(LengthOf(Line(E, O)), 2y+19); "
}
] |
geometry3k/train/1036/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); PointLiesOnCircle(B, Circle(A, radius_)); "
}
] |
geometry3k/train/1042/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)), 2y+5); Equals(LengthOf(Line(B, E)), y+3); Equals(LengthOf(Line(A, E)), 2x+6); Equals(LengthOf(Line(C, E)), 4y-9); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(E, Line(C, D)); "
}
] |
geometry3k/train/1044/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)), 25); Equals(LengthOf(Line(A, C)), 12); "
}
] |
geometry3k/train/1048/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(D, E), Line(B, E)); Equals(LengthOf(Line(D, A)), 10); Equals(LengthOf(Line(E, D)), 5); Equals(LengthOf(Line(D, C)), 4); PointLiesOnLine(E, Line(C, B)); "
}
] |
geometry3k/train/1050/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, G)), 78); Equals(MeasureOf(Angle(G, D, E)), x); PointLiesOnLine(D, Line(C, E)); "
}
] |
geometry3k/train/1052/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(Q, R, S)), 136); Equals(MeasureOf(Angle(Q, T, S)), 68); Equals(LengthOf(Line(S, R)), LengthOf(Line(R, Q))); Equals(LengthOf(Line(S, T)), LengthOf(Line(T, Q))); "
}
] |
geometry3k/train/1056/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)), 13); Equals(MeasureOf(Angle(C, E, A)), 18); Equals(MeasureOf(Angle(E, A, C)), 141); Equals(LengthOf(Line(C, E)), x); "
}
] |
geometry3k/train/1057/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, X, A)), 3x); Equals(MeasureOf(Angle(A, X, B)), 7x+10); Equals(MeasureOf(Angle(B, X, C)), 90); PointLiesOnCircle(A, Circle(X, radius_)); PointLiesOnCircle(B, Circle(X, radius_)); PointLiesOnCircle(C, Circle(X, radius_)); "
}
] |
geometry3k/train/1063/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, F, C)), 72); Equals(MeasureOf(Angle(D, F, A)), 2a-5); Equals(MeasureOf(Angle(C, F, D)), 4a-1); PointLiesOnCircle(D, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(B, Circle(F, radius_)); "
}
] |
geometry3k/train/1064/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)), y); Equals(MeasureOf(Angle(C, B, A)), 45); Equals(LengthOf(Line(A, C)), x); Equals(LengthOf(Line(B, C)), 7\\sqrt{2}); Perpendicular(Line(A, C), Line(C, B)); "
}
] |
geometry3k/train/1065/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(Y, Z)), 11.2); Equals(MeasureOf(Angle(X, Y, Z)), 55); PointLiesOnCircle(X, Circle(Y, radius_)); PointLiesOnCircle(Z, Circle(Y, radius_)); "
}
] |
geometry3k/train/1066/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(K, J, L)), 4x-13); Equals(MeasureOf(Angle(W, Z, Y)), 44); Equals(MeasureOf(Angle(Y, W, Z)), 71); Equals(MeasureOf(Angle(J, K, L)), y); "
}
] |
geometry3k/train/1067/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(MeasureOf(Angle(C, A, B)), 20); Equals(MeasureOf(Angle(A, C, B)), 135); Equals(LengthOf(Line(B, C)), 18); "
}
] |
geometry3k/train/1070/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(D, C)), y); Equals(LengthOf(Line(A, D)), z); Equals(LengthOf(Line(B, C)), 12); Equals(LengthOf(Line(B, D)), 4); Perpendicular(Line(D, B), Line(D, C)); Perpendicular(Line(C, B), Line(C, A)); PointLiesOnLine(D, Line(B, A)); "
}
] |
geometry3k/train/1072/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)), 37.5); Equals(LengthOf(Line(B, C)), x); Equals(LengthOf(Line(A, C)), 20); Perpendicular(Line(A, B), Line(A, C)); "
}
] |
geometry3k/train/1073/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, A, D)), 45); Equals(MeasureOf(Angle(B, E, D)), 45); Equals(MeasureOf(Angle(D, B, F)), 45); Equals(MeasureOf(Angle(A, C, D)), 45); Equals(LengthOf(Line(F, D)), x); Equals(LengthOf(Line(C, D)), 6); Perpendicular(Line(D, E), Line(A, E)); Perpendicular(Line(C, A), Line(A, D)); Perpendicular(Line(E, B), Line(D, B)); Perpendicular(Line(E, D), Line(C, D)); Perpendicular(Line(B, F), Line(D, F)); PointLiesOnLine(D, Line(F, C)); "
}
] |
geometry3k/train/1076/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)), 75); Equals(LengthOf(Line(B, C)), 40); Perpendicular(Line(A, B), Line(B, C)); "
}
] |
geometry3k/train/1077/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)), 30); Equals(LengthOf(Line(C, A)), 16); Perpendicular(Line(A, B), Line(A, C)); PointLiesOnLine(D, Line(B, C)); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(B, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); "
}
] |
geometry3k/train/1078/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)), 4); Equals(LengthOf(Line(H, K)), 5); Equals(LengthOf(Line(L, K)), x); Equals(LengthOf(Line(H, N)), 2); PointLiesOnLine(N, Line(H, M)); PointLiesOnLine(J, Line(H, K)); PointLiesOnLine(L, Line(M, K)); PointLiesOnCircle(L, Circle(O, radius_)); PointLiesOnCircle(J, Circle(O, radius_)); PointLiesOnCircle(N, Circle(O, radius_)); "
}
] |
geometry3k/train/1081/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)), 43); Equals(LengthOf(Line(C, A)), x); Equals(LengthOf(Line(D, A)), 4); Equals(LengthOf(Line(B, D)), 6); Equals(MeasureOf(Angle(B, C, D)), MeasureOf(Angle(D, C, A))); PointLiesOnLine(D, Line(A, B)); "
}
] |
geometry3k/train/1083/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)), 13); Equals(LengthOf(Line(A, C)), 10); Equals(MeasureOf(Angle(C, B, D)), 45); "
}
] |
geometry3k/train/1087/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(DiameterOf(Cirle(A))), 12); PointLiesOnCircle(B, Circle(A, radius_)); PointLiesOnCircle(C, Circle(A, radius_)); PointLiesOnCircle(D, Circle(A, radius_)); PointLiesOnCircle(I, Circle(A, radius_)); PointLiesOnCircle(E, Circle(A, radius_)); "
}
] |
geometry3k/train/1088/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(Y, W, X)), 52); Equals(MeasureOf(Angle(W, X, Y)), 6y-2); Equals(MeasureOf(Angle(W, Y, X)), 4x+20); Equals(LengthOf(Line(W, X)), LengthOf(Line(W, Y))); "
}
] |
geometry3k/train/1089/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, M)), 4.5); Equals(MeasureOf(Angle(E, M, A)), 4x+1); Equals(MeasureOf(Angle(D, M, A)), 5x-5); Equals(LengthOf(Line(M, D)), 4.5); Equals(LengthOf(Line(A, C)), LengthOf(Line(D, A))); PointLiesOnLine(D, Line(B, M)); PointLiesOnLine(C, Line(E, M)); PointLiesOnLine(A, Line(F, M)); "
}
] |
geometry3k/train/1090/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)), \\frac{8}{9}); Equals(LengthOf(Line(B, C)), \\frac{4}{9}); Equals(LengthOf(Line(A, C)), x); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/1091/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(MeasureOf(Angle(D, B, A)), y); Equals(LengthOf(Line(B, A)), 17); Perpendicular(Line(D, A), Line(B, D)); Equals(LengthOf(Line(B, D)), LengthOf(Line(A, C))); Equals(LengthOf(Line(A, C)), LengthOf(Line(A, D))); Equals(LengthOf(Line(C, A)), LengthOf(Line(C, B))); "
}
] |
geometry3k/train/1092/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(D, C)), 12); Equals(LengthOf(Line(B, A)), 12); PointLiesOnLine(B, Line(A, C)); PointLiesOnLine(E, Line(A, C)); PointLiesOnLine(B, Line(C, E)); PointLiesOnLine(E, Line(B, A)); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(B, Circle(E, radius_)); "
}
] |
geometry3k/train/1094/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)), 2); Equals(MeasureOf(Angle(A, B, C)), 98); PointLiesOnCircle(A, Circle(B, radius_)); PointLiesOnCircle(C, Circle(B, radius_)); "
}
] |
geometry3k/train/1095/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, U)), x+2); Equals(LengthOf(Line(V, U)), 3); Equals(LengthOf(Line(S, T)), 4); Equals(LengthOf(Line(S, R)), 2x); Perpendicular(Line(S, T), Line(U, S)); Perpendicular(Line(V, R), Line(V, U)); PointLiesOnLine(S, Line(T, R)); PointLiesOnLine(U, Line(T, V)); "
}
] |
geometry3k/train/1096/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)), a); Equals(LengthOf(Line(A, F)), 12); Equals(LengthOf(Line(G, D)), 12); Equals(LengthOf(Line(D, A)), 12); Equals(LengthOf(Line(D, H)), 6); Equals(MeasureOf(Angle(H, D, G)), 60); Perpendicular(Line(G, H), Line(H, D)); PointLiesOnLine(H, Line(A, D)); "
}
] |
geometry3k/train/1097/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)), 12); Equals(LengthOf(Line(A, B)), x); Equals(LengthOf(Line(B, C)), 8); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/1098/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)), 5); Equals(LengthOf(Line(O, N)), 3+\\frac{3}{5}); Equals(LengthOf(Line(N, M)), 6); Parallel(Line(P, O), Line(N, Q)); PointLiesOnLine(N, Line(O, M)); PointLiesOnLine(Q, Line(P, M)); "
}
] |
geometry3k/train/1099/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, W)), x); Equals(MeasureOf(Angle(S, W, T)), 63); Equals(MeasureOf(Angle(T, S, W)), 31); Equals(LengthOf(Line(S, W)), 14); "
}
] |
geometry3k/train/1100/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, T)), LengthOf(Line(U, V))); Equals(MeasureOf(Arc(N, V)), 5x-27); Equals(MeasureOf(Arc(S, M)), 2x); PointLiesOnCircle(U, Circle(N, radius_)); PointLiesOnCircle(V, Circle(N, radius_)); PointLiesOnCircle(S, Circle(M, radius_)); PointLiesOnCircle(T, Circle(M, radius_)); "
}
] |
geometry3k/train/1101/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)), 5); Equals(LengthOf(Line(D, B)), 10); PointLiesOnLine(G, Line(A, C)); PointLiesOnLine(F, Line(C, B)); PointLiesOnLine(E, Line(D, B)); PointLiesOnCircle(E, Circle(O, radius_)); PointLiesOnCircle(F, Circle(O, radius_)); PointLiesOnCircle(G, Circle(O, radius_)); "
}
] |
geometry3k/train/1102/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, M)), 15); Equals(LengthOf(Line(T, P)), x); Equals(LengthOf(Line(Q, T)), 8); Equals(LengthOf(Line(Q, N)), 4); PointLiesOnLine(P, Line(T, M)); PointLiesOnLine(Q, Line(T, N)); "
}
] |
geometry3k/train/1103/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)), 5); Equals(LengthOf(Line(A, B)), x-2); Equals(LengthOf(Line(A, D)), x); Equals(LengthOf(Line(D, G)), 75); PointLiesOnLine(B, Line(E, A)); PointLiesOnLine(D, Line(A, G)); "
}
] |
geometry3k/train/1106/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)), 8); Equals(LengthOf(Line(C, B)), 10); Equals(LengthOf(Line(D, C)), 9); Equals(LengthOf(Line(E, D)), x); PointLiesOnLine(E, Line(F, C)); PointLiesOnLine(D, Line(C, F)); PointLiesOnLine(D, Line(E, C)); PointLiesOnLine(B, Line(C, A)); PointLiesOnLine(E, Line(D, F)); PointLiesOnCircle(A, Circle(O, radius_)); PointLiesOnCircle(B, Circle(O, radius_)); PointLiesOnCircle(E, Circle(P, radius_)); PointLiesOnCircle(D, Circle(P, radius_)); PointLiesOnCircle(H, Circle(P, radius_)); "
}
] |
geometry3k/train/1107/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)), 70); Equals(LengthOf(Line(D, B)), 70); Equals(MeasureOf(Angle(E, D, C)), 60); Perpendicular(Line(E, C), Line(D, E)); "
}
] |
geometry3k/train/1108/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, Q)), 5); Equals(LengthOf(Line(R, T)), 3); Equals(LengthOf(Line(S, T)), 12); Equals(LengthOf(Line(S, V)), x); Perpendicular(Line(V, T), Line(Q, V)); Perpendicular(Line(T, S), Line(T, R)); PointLiesOnLine(T, Line(S, V)); PointLiesOnLine(R, Line(Q, S)); "
}
] |
geometry3k/train/1109/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)), 155); Equals(MeasureOf(Angle(A, B, D)), 125); Equals(MeasureOf(Angle(C, B, A)), x); PointLiesOnCircle(A, Circle(B, radius_)); PointLiesOnCircle(C, Circle(B, radius_)); PointLiesOnCircle(D, Circle(B, radius_)); "
}
] |
geometry3k/train/1111/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)), y); Equals(LengthOf(Line(A, C)), 8); Equals(MeasureOf(Angle(A, B, C)), 30); Equals(LengthOf(Line(B, C)), x); Perpendicular(Line(A, C), Line(C, B)); "
}
] |
geometry3k/train/1112/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)), 8); Equals(LengthOf(Line(T, S)), 12); Perpendicular(Line(R, S), Line(T, S)); "
}
] |
geometry3k/train/1115/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(I, C)), 10); Equals(LengthOf(Line(I, A)), 10); Equals(LengthOf(Line(I, D)), 13); Equals(LengthOf(Line(B, I)), 13); Perpendicular(Line(D, I), Line(I, C)); PointLiesOnLine(I, Line(A, C)); PointLiesOnLine(I, Line(D, B)); "
}
] |
geometry3k/train/1119/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, D)), x); Equals(MeasureOf(Arc(A, C)), 68); Equals(MeasureOf(Arc(D, F)), 24); PointLiesOnLine(D, Line(A, B)); PointLiesOnLine(F, Line(B, C)); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); "
}
] |
geometry3k/train/1121/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, A)), 4); PointLiesOnCircle(N, Circle(A, radius_)); "
}
] |
geometry3k/train/1122/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, M)), 8); Equals(LengthOf(Line(K, M)), 16); Perpendicular(Line(M, K), Line(L, M)); Perpendicular(Line(M, L), Line(K, L)); PointLiesOnLine(M, Line(J, K)); "
}
] |
geometry3k/train/1124/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, D, A)), x); Equals(MeasureOf(Angle(B, C, E)), 116); Equals(MeasureOf(Angle(D, E, C)), 72); Equals(LengthOf(Line(C, E)), LengthOf(Line(B, C))); Equals(LengthOf(Line(A, D)), LengthOf(Line(D, E))); PointLiesOnLine(E, Line(B, A)); "
}
] |
geometry3k/train/1125/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(MeasureOf(Angle(B, D, C)), 58); Equals(LengthOf(Line(B, D)), 6); Perpendicular(Line(A, C), Line(A, B)); Equals(LengthOf(Line(C, B)), LengthOf(Line(C, D))); PointLiesOnLine(A, Line(B, D)); "
}
] |
geometry3k/train/1126/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(F, C)); PointLiesOnLine(E, Line(C, A)); PointLiesOnLine(D, Line(C, B)); PointLiesOnLine(Q, Line(A, D)); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(Q, Line(B, E)); "
}
] |
geometry3k/train/1127/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)), 10); Equals(LengthOf(Line(D, E)), x); Equals(LengthOf(Line(D, C)), 15); Equals(LengthOf(Line(A, D)), 12); 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_)); "
}
] |
geometry3k/train/1129/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(G, L), Line(K, L)); PointLiesOnLine(L, Line(G, H)); PointLiesOnLine(K, Line(G, J)); PointLiesOnLine(K, Line(H, F)); PointLiesOnCircle(G, Circle(K, radius_)); PointLiesOnCircle(H, Circle(K, radius_)); PointLiesOnCircle(F, Circle(K, radius_)); PointLiesOnCircle(J, Circle(K, radius_)); "
}
] |
geometry3k/train/1131/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+2); Equals(LengthOf(Line(B, A)), 6x-10); Equals(LengthOf(Line(E, C)), 3y+5); Equals(LengthOf(Line(E, A)), 7y-11); Perpendicular(Line(C, D), Line(E, C)); Perpendicular(Line(B, E), Line(E, A)); Equals(LengthOf(Line(B, D)), LengthOf(Line(A, B))); PointLiesOnLine(E, Line(A, C)); PointLiesOnLine(B, Line(A, D)); "
}
] |
geometry3k/train/1136/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)), 8); Equals(LengthOf(Line(T, Q)), 8); Equals(MeasureOf(Angle(S, Q, R)), 43); Perpendicular(Line(R, S), Line(S, Q)); Perpendicular(Line(T, R), Line(Q, T)); "
}
] |
geometry3k/train/1138/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, C, B)), 82); Equals(MeasureOf(Angle(D, B, C)), 28); Equals(MeasureOf(Angle(C, E, B)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(D, E, A)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(A, D, E)), 68); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(D, A, C))); PointLiesOnLine(E, Line(C, A)); PointLiesOnLine(E, Line(D, B)); "
}
] |
geometry3k/train/1139/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(MeasureOf(Angle(D, C, A)), 60); Equals(MeasureOf(Angle(C, D, A)), 60); Equals(LengthOf(Line(B, A)), y); Equals(LengthOf(Line(A, C)), 11); Equals(MeasureOf(Angle(B, A, C)), 30); Perpendicular(Line(D, B), Line(A, B)); PointLiesOnLine(B, Line(D, C)); "
}
] |
geometry3k/train/1140/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)), 4); Equals(LengthOf(Line(C, A)), 9); Equals(LengthOf(Line(E, A)), x); Equals(LengthOf(Line(E, B)), 8); PointLiesOnLine(E, Line(B, A)); PointLiesOnLine(A, Line(B, F)); PointLiesOnLine(E, Line(F, B)); PointLiesOnLine(A, Line(D, C)); PointLiesOnLine(A, Line(E, F)); PointLiesOnCircle(B, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); "
}
] |
geometry3k/train/1145/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)), 16); Equals(MeasureOf(Angle(C, B, A)), 45); Equals(LengthOf(Line(A, C)), x); Perpendicular(Line(A, B), Line(A, C)); "
}
] |
geometry3k/train/1147/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(P, Q)), 37); Equals(LengthOf(Line(R, Q)), 58); Perpendicular(Line(P, Q), Line(R, P)); "
}
] |
geometry3k/train/1148/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)), 50); Equals(LengthOf(Line(A, C)), 14); Equals(LengthOf(Line(B, C)), x); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/1150/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, G, B)), MeasureOf(Angle(19))); Equals(MeasureOf(Angle(B, G, D)), MeasureOf(Angle(20))); PointLiesOnLine(G, Line(B, E)); PointLiesOnLine(G, Line(C, D)); "
}
] |
geometry3k/train/1153/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)), 5); Equals(LengthOf(Line(O, B)), 21.5); Equals(LengthOf(Line(O, C)), 8); Equals(LengthOf(Line(A, C)), 15); Perpendicular(Line(C, A), Line(O, C)); PointLiesOnLine(A, Line(C, B)); "
}
] |
geometry3k/train/1155/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, C)), p); Equals(MeasureOf(Angle(D, A, O)), m); Equals(MeasureOf(Angle(C, O, A)), n); PointLiesOnLine(A, Line(B, D)); PointLiesOnLine(O, Line(B, C)); "
}
] |
geometry3k/train/1157/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(B, Line(D, A)); PointLiesOnLine(C, Line(A, F)); "
}
] |
geometry3k/train/1158/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)), 6); Equals(LengthOf(Line(Y, A)), x); Equals(LengthOf(Line(B, C)), y); Equals(MeasureOf(Angle(A, C, B)), 45); Perpendicular(Line(A, C), Line(A, B)); Perpendicular(Line(C, Y), Line(A, Y)); PointLiesOnLine(Y, Line(B, C)); "
}
] |
geometry3k/train/1159/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, L, I)), 59); Perpendicular(Line(L, J), Line(L, I)); PointLiesOnLine(L, Line(G, I)); PointLiesOnLine(L, Line(H, K)); PointLiesOnCircle(H, Circle(L, radius_)); PointLiesOnCircle(I, Circle(L, radius_)); PointLiesOnCircle(J, Circle(L, radius_)); PointLiesOnCircle(K, Circle(L, radius_)); PointLiesOnCircle(G, Circle(L, radius_)); "
}
] |
geometry3k/train/1161/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)), 3); Equals(LengthOf(Line(A, B)), 4); Perpendicular(Line(A, C), Line(A, B)); "
}
] |
geometry3k/train/1162/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, H)), 6); Equals(LengthOf(Line(G, H)), 1); Equals(LengthOf(Line(G, E)), 2); Equals(LengthOf(Line(B, E)), 2); Equals(LengthOf(Line(F, B)), 3); Equals(LengthOf(Line(A, C)), 8); Equals(LengthOf(Line(F, D)), 5); Equals(LengthOf(Line(A, D)), 11); Perpendicular(Line(C, A), Line(H, C)); Perpendicular(Line(H, C), Line(G, H)); Perpendicular(Line(B, E), Line(G, E)); Perpendicular(Line(D, F), Line(B, F)); Perpendicular(Line(D, A), Line(A, C)); Perpendicular(Line(A, D), Line(F, D)); "
}
] |
geometry3k/train/1163/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)), 5); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(B, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); "
}
] |
geometry3k/train/1166/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(N, Q), Line(K, N)); Perpendicular(Line(M, R), Line(P, M)); PointLiesOnLine(Q, Line(R, P)); PointLiesOnLine(R, Line(M, L)); PointLiesOnLine(Q, Line(N, M)); PointLiesOnLine(P, Line(M, K)); PointLiesOnLine(N, Line(L, K)); "
}
] |
geometry3k/train/1168/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, O, A)), 2x-5); Equals(MeasureOf(Angle(J, L, E)), 3x+10); Equals(MeasureOf(Angle(I, D, O)), 5x); Equals(MeasureOf(Angle(D, B, H)), 2x); Equals(MeasureOf(Angle(K, J, B)), 6x-5); PointLiesOnLine(O, Line(D, A)); PointLiesOnLine(L, Line(O, E)); PointLiesOnLine(D, Line(I, B)); PointLiesOnLine(B, Line(H, J)); PointLiesOnLine(J, Line(L, K)); "
}
] |
geometry3k/train/1169/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)), 33); Equals(LengthOf(Line(E, C)), 25); Equals(LengthOf(Line(E, D)), x); Perpendicular(Line(C, E), Line(E, D)); PointLiesOnLine(E, Line(A, C)); PointLiesOnLine(E, Line(D, B)); "
}
] |
geometry3k/train/1170/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, W)), 7); Equals(MeasureOf(Angle(X, Z, D)), 41); Equals(MeasureOf(Angle(B, Z, C)), 41); Perpendicular(Line(W, X), Line(W, D)); PointLiesOnLine(Y, Line(Z, B)); PointLiesOnLine(X, Line(Z, C)); PointLiesOnLine(W, Line(Z, D)); "
}
] |
geometry3k/train/1174/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)), x); Equals(LengthOf(Line(A, C)), 18); Equals(MeasureOf(Angle(C, A, D)), 52); "
}
] |
geometry3k/train/1175/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, X)), 12x+2); Equals(LengthOf(Line(X, C)), 10x); Equals(LengthOf(Line(E, X)), x+1); Equals(LengthOf(Line(B, X)), x); PointLiesOnLine(X, Line(B, D)); PointLiesOnLine(X, Line(E, C)); PointLiesOnCircle(B, Circle(A, radius_)); PointLiesOnCircle(C, Circle(A, radius_)); PointLiesOnCircle(D, Circle(A, radius_)); PointLiesOnCircle(E, Circle(A, radius_)); "
}
] |
geometry3k/train/1176/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)), MeasureOf(Angle(11))); Equals(MeasureOf(Angle(K, F, A)), MeasureOf(Angle(12))); "
}
] |
geometry3k/train/1177/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)), 5); Equals(LengthOf(Line(Q, T)), x); "
}
] |
geometry3k/train/1182/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(S, T, P)), 150); Perpendicular(Line(R, S), Line(T, S)); PointLiesOnLine(T, Line(R, P)); "
}
] |
geometry3k/train/1184/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)), 4); Equals(LengthOf(Line(C, B)), x); Equals(LengthOf(Line(C, D)), x+2); PointLiesOnLine(C, Line(D, B)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(A, Circle(E, radius_)); "
}
] |
geometry3k/train/1186/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, D, H)), 28); Equals(LengthOf(Line(G, F)), LengthOf(Line(F, H))); Equals(LengthOf(Line(A, H)), LengthOf(Line(D, G))); PointLiesOnLine(G, Line(H, D)); "
}
] |
geometry3k/train/1187/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, A, C)), 19); Equals(LengthOf(Line(A, C)), x); Equals(MeasureOf(Angle(A, B, C)), 111); Equals(LengthOf(Line(B, C)), 41); "
}
] |
geometry3k/train/1188/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(Y, K), Line(P, K)); Perpendicular(Line(P, L), Line(L, Z)); Perpendicular(Line(J, P), Line(J, Y)); Equals(LengthOf(Line(P, Z)), 20); Equals(LengthOf(Line(J, Z)), 12); Equals(MeasureOf(Angle(P, K, X)), 31); Equals(MeasureOf(Angle(J, Y, P)), 27); PointLiesOnLine(J, Line(Z, Y)); PointLiesOnLine(L, Line(Z, X)); PointLiesOnLine(K, Line(X, Y)); "
}
] |
geometry3k/train/1189/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, C)), x); Equals(MeasureOf(Angle(B, A, D)), x); Equals(MeasureOf(Angle(D, C, B)), 2x); Equals(MeasureOf(Angle(C, B, A)), 2x); "
}
] |
geometry3k/train/1190/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, J)), 8); PointLiesOnLine(K, Line(Z, Y)); PointLiesOnLine(P, Line(Z, J)); PointLiesOnLine(J, Line(Y, X)); PointLiesOnLine(P, Line(Y, L)); PointLiesOnLine(P, Line(X, K)); "
}
] |
geometry3k/train/1191/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, C)), x); Equals(LengthOf(Line(B, C)), 36); Equals(LengthOf(Line(A, B)), 59); Equals(LengthOf(Line(A, C)), 39); "
}
] |
geometry3k/train/1193/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(G, A)), 5x); Equals(MeasureOf(Angle(D, B, E)), 25); Equals(MeasureOf(Arc(D, E)), 90); PointLiesOnLine(A, Line(B, D)); PointLiesOnLine(G, Line(B, E)); PointLiesOnCircle(A, Circle(C, radius_)); PointLiesOnCircle(D, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); PointLiesOnCircle(G, Circle(C, radius_)); "
}
] |
geometry3k/train/1194/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(B, C)), x); Equals(LengthOf(Line(A, B)), 12); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/1195/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(E, C)), 125); Equals(MeasureOf(Angle(C, B, A)), x); Equals(MeasureOf(Arc(A, D)), 117); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(B, Line(A, E)); PointLiesOnLine(F, Line(A, E)); PointLiesOnLine(B, Line(E, F)); PointLiesOnLine(B, Line(C, D)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(D, Circle(F, radius_)); PointLiesOnCircle(E, Circle(F, radius_)); "
}
] |
geometry3k/train/1196/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, F)), 120); Equals(MeasureOf(Angle(B, E, H)), 160); Equals(MeasureOf(Angle(E, A, D)), x); Perpendicular(Line(D, A), Line(B, D)); PointLiesOnLine(E, Line(B, A)); PointLiesOnLine(G, Line(B, D)); PointLiesOnLine(G, Line(C, E)); PointLiesOnLine(B, Line(L, F)); PointLiesOnLine(E, Line(G, H)); PointLiesOnLine(E, Line(C, H)); PointLiesOnLine(G, Line(H, C)); "
}
] |
geometry3k/train/1197/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)), 20); Equals(LengthOf(Line(D, E)), 24); Perpendicular(Line(B, E), Line(C, E)); Equals(LengthOf(Line(A, D)), LengthOf(Line(A, B))); Equals(LengthOf(Line(D, A)), LengthOf(Line(D, C))); Equals(LengthOf(Line(A, D)), LengthOf(Line(C, B))); PointLiesOnLine(E, Line(A, C)); PointLiesOnLine(E, Line(D, B)); "
}
] |
geometry3k/train/1198/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(E, Line(A, D)); PointLiesOnLine(B, Line(A, C)); "
}
] |
geometry3k/train/1199/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, R, T)), 4x); Equals(MeasureOf(Angle(R, W, Z)), 45); Equals(MeasureOf(Angle(W, Z, T)), 2x+30); PointLiesOnCircle(R, Circle(O, radius_)); PointLiesOnCircle(T, Circle(O, radius_)); PointLiesOnCircle(W, Circle(O, radius_)); PointLiesOnCircle(Z, Circle(O, radius_)); "
}
] |
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