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pependicularity wanted, touchpoints of incircle related

Source: 2013 Thailand October Camp Geometry Exam p2

October 22, 2020
geometryperpendicularincircle

Problem Statement

In a triangle ABCABC, the incircle with incenter II is tangent to BCBC at A1,CAA_1, CA at B1B_1, and ABAB at C1C_1. Denote the intersection of AA1AA_1 and BB1BB_1 by GG, the intersection of ACAC and A1C1A_1C_1 by XX, and the intersection of BCBC and B1C1B_1C_1 by YY . Prove that IG⊥XYIG \perp XY .
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