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Iran TST 2009-Day3-P3

Source:

May 16, 2009
geometrygeometric transformationhomothetytrigonometrygraphing linesslopeIran Lemma

Problem Statement

In triangle ABCABC, DD, EE and FF are the points of tangency of incircle with the center of II to BCBC, CACA and ABAB respectively. Let MM be the foot of the perpendicular from DD to EFEF. PP is on DMDM such that DP=MPDP = MP. If HH is the orthocenter of BICBIC, prove that PHPH bisects EF EF.
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