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Ten Points

Source: 2002 National High School Mathematics League, Exam One, Problem 9

March 16, 2020
geometry3D geometrypyramid

Problem Statement

Points P1,P2,P3,P4P_1,P_2,P_3,P_4 are vertexes of a regular triangular pyramid, and P5,P6,P7,P8,P9,P10P_5,P_6,P_7,P_8,P_9,P_{10} midpoints of edges. The number of groups (P1,Pi,Pj,Pk)(1<i<j<k≤10)(P_1,P_i,P_j,P_k)(1<i<j<k\leq10) that P1,Pi,Pj,PkP_1,P_i,P_j,P_k are coplane is________.
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