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no of triangles of area 1 at vertices of convex n-gon <= 1 /3 n (2n-5)

Source: Tuymaada Junior 2006 p3

May 12, 2019
geometryconvex polygonarea of a trianglecombinatorial geometry

Problem Statement

Given a convex n n -gon (n≥5 n \geq 5 ). Prove that the number of triangles of area 11 with vertices at the vertices of the n n -gon does not exceed 13n(2n−5) \frac{1}{3} n (2n-5) .
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