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Argentina Cono Sur TST 2013. Problem 5

Source:

January 3, 2015
ratiogeometry

Problem Statement

Let ABCABC be an equilateral triangle and DD a point on side ACAC. Let EE be a point on BCBC such that DE⊥BCDE \perp BC, FF on ABAB such that EF⊥ABEF \perp AB, and GG on ACAC such that FG⊥ACFG \perp AC. Lines FGFG and DEDE intersect in PP. If MM is the midpoint of BCBC, show that BPBP bisects AMAM.
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