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1

Part of 1983 Polish MO Finals

Problems(1)

even no of triangles P_iP_jP_k containing interior P in convex n-gon

Source: 1983 Polish MO Finals p1

2/25/2020
On the plane are given a convex nn-gon P1P2....PnP_1P_2....P_n and a point QQ inside it, not lying on any of its diagonals. Prove that if nn is even, then the number of triangles PiPjPkP_iP_jP_k containing the point QQ is even.
combinatorial geometrycombinatoricspolygonTriangles