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prove three points collinear

Source: 2012 China TST P2

March 15, 2012
geometrygeometry unsolved

Problem Statement

Given a scalene triangle ABCABC. Its incircle touches BC,AC,ABBC,AC,AB at D,E,FD,E,F respectvely. Let L,M,NL,M,N be the symmetric points of DD with EFEF,of EE with FDFD,of FF with DEDE,respectively. Line ALAL intersects BCBC at PP,line BMBM intersects CACA at QQ,line CNCN intersects ABAB at RR. Prove that P,Q,RP,Q,R are collinear.
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