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Diagonal of a convex polygon

Source: 2002 Austrian-Polish, problem 2

September 23, 2006
geometryconvex polygonconvex

Problem Statement

Let P1P2…P2nP_{1}P_{2}\dots P_{2n} be a convex polygon with an even number of corners. Prove that there exists a diagonal PiPjP_{i}P_{j} which is not parallel to any side of the polygon.
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