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The same area

Source: 2017 Indonesia MO, Problem 7

July 7, 2017
geometryparallelogram

Problem Statement

Let ABCDABCD be a parallelogram. EE and FF are on BC,CDBC, CD respectively such that the triangles ABEABE and BCFBCF have the same area. Let BDBD intersect AE,AFAE, AF at M,NM, N respectively. Prove there exists a triangle whose side lengths are BM,MN,NDBM, MN, ND.
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