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Circumcircles of PDL,PEM,PFN meet at two points

Source: China Team Selection Test 2016 Test 2 Day 1 Q1

March 20, 2016
geometrycircumcirclegeometric transformationreflection

Problem Statement

PP is a point in the interior of acute triangle ABCABC. D,E,FD,E,F are the reflections of PP across BC,CA,ABBC,CA,AB respectively. Rays AP,BP,CPAP,BP,CP meet the circumcircle of △ABC\triangle ABC at L,M,NL,M,N respectively. Prove that the circumcircles of △PDL,△PEM,△PFN\triangle PDL,\triangle PEM,\triangle PFN meet at a point TT different from PP.
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