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A Bunch of Perpendicular Lines

Source: OMM 2009 5

July 15, 2014
geometry unsolvedgeometry

Problem Statement

Consider a triangle ABCABC and a point MM on side BCBC. Let PP be the intersection of the perpendiculars from MM to ABAB and from BB to BCBC, and let QQ be the intersection of the perpendiculars from MM to ACAC and from CC to BCBC. Show that PQPQ is perpendicular to AMAM if and only if MM is the midpoint of BCBC.
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