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Easy geometry

Source: Serbia Math Olympiad 2016

April 2, 2016
geometryincenter

Problem Statement

Let ABCABC be a triangle, and II the incenter, MM midpoint of BC BC , D D the touch point of incircle and BC BC . Prove that perpendiculars from M,D,AM, D, A to AI,IM,BCAI, IM, BC respectively are concurrent
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