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Prove Collinearity

Source: 2012 USAMO Day 2 #5 and USAJMO Day 2 #6

April 25, 2012
geometrygeometric transformationUSA(J)MOUSAMO2012 USAJMO2012 USAMO

Problem Statement

Let PP be a point in the plane of △ABC\triangle ABC, and γ\gamma a line passing through PP. Let A′,B′,C′A', B', C' be the points where the reflections of lines PA,PB,PCPA, PB, PC with respect to γ\gamma intersect lines BC,AC,ABBC, AC, AB respectively. Prove that A′,B′,C′A', B', C' are collinear.
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