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Collinearity of three points

Source: Korean Summer Program Practice Test 2016 2

August 17, 2016
geometry

Problem Statement

Let the incircle of triangle ABCABC meet the sides BCBC, CACA, ABAB at DD, EE, FF, and let the AA-excircle meet the lines BCBC, CACA, ABAB at PP, QQ, RR. Let the line passing through AA and perpendicular to BCBC meet the lines EFEF, QRQR at KK, LL. Let the intersection of LDLD and EFEF be SS, and the intersection of KPKP and QRQR be TT. Prove that AA, SS, TT are collinear.
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