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Mexican geometry - Portuguese MO, Problem 5, 2008

Source:

August 31, 2010
geometrygeometry proposed

Problem Statement

Let ABCABC be a right-angled triangle in AA such that AB<ACAB<AC. Let MM be the midpoint of BCBC and let DD be the intersection of ACAC with the perpendicular line to BCBC which passes through MM. Let EE be the intersection point of the parallel line to ACAC which passes through MM with the perpendicular line to BDBD which passes through BB. Prove that triangles AEMAEM and MCAMCA are similar if and only if ∠ABC=60∘\angle ABC=60^{\circ}.
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