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Some geometry

Source: St Petersburg Olympiad 2010, Grade 9, P7

September 14, 2017
geometry

Problem Statement

Incircle of ABCABC tangent AB,AC,BCAB,AC,BC in C1,B1,A1C_1,B_1,A_1. AA1AA_1 intersect incircle in EE. NN is midpoint B1A1B_1A_1. MM is symmetric to NN relatively AA1AA_1. Prove that ∠EMC=90\angle EMC= 90
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