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Reflection about.... perpendicular bisector?

Source: Sharygin 2019 Finals Day 1 Grade 9 P2

July 30, 2019
geometrySharygin Geometry Olympiadperpendicular bisector

Problem Statement

Let PP be a point on the circumcircle of triangle ABCABC. Let A1A_1 be the reflection of the orthocenter of triangle PBCPBC about the reflection of the perpendicular bisector of BCBC. Points B1B_1 and C1C_1 are defined similarly. Prove that A1,B1,C1A_1,B_1,C_1 are collinear.
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