Problem

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Tags: geometry, geometric transformation, homothety, trigonometry, graphing lines, slope, Iran Lemma



In triangle ABC, D, E and F are the points of tangency of incircle with the center of I to BC, CA and AB respectively. Let M be the foot of the perpendicular from D to EF. P is on DM such that DP=MP. If H is the orthocenter of BIC, prove that PH bisects EF.