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In a convex pentagon ABCDE, 4 segments are concurrent

Source: Balkan MO 1996, Problem 3

April 24, 2006
geometrytrigonometryvectorgeometry proposed

Problem Statement

In a convex pentagon ABCDEABCDE, the points MM, NN, PP, QQ, RR are the midpoints of the sides ABAB, BCBC, CDCD, DEDE, EAEA, respectively. If the segments APAP, BQBQ, CRCR and DMDM pass through a single point, prove that ENEN contains that point as well. Yugoslavia
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