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A circle through another's centre

Source: 2015 China TST 1 Day 1 Q1

March 14, 2015
geometryTST

Problem Statement

The circle Γ\Gamma through AA of triangle ABCABC meets sides AB,ACAB,AC at EE,FF respectively, and circumcircle of ABCABC at PP. Prove: Reflection of PP across EFEF is on BCBC if and only if Γ\Gamma passes through OO (the circumcentre of ABCABC).
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