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collinear orthocenters

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August 20, 2012
geometryincentertrigonometryrhombusgeometry proposed

Problem Statement

A point MM lies on the side BCBC of square ABCDABCD. Let XX, YY , and ZZ be the incenters of triangles ABMABM, CMDCMD, and AMDAMD respectively. Let HxH_x, HyH_y, and HzH_z be the orthocenters of triangles AXBAXB, CYDCY D, and AZDAZD. Prove that HxH_x, HyH_y, and HzH_z are collinear.
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