Problem

Source: Sharygin 2019 Finals Day 1 Grade 9 P2

Tags: geometry, Sharygin Geometry Olympiad, perpendicular bisector



Let $P$ be a point on the circumcircle of triangle $ABC$. Let $A_1$ be the reflection of the orthocenter of triangle $PBC$ about the reflection of the perpendicular bisector of $BC$. Points $B_1$ and $C_1$ are defined similarly. Prove that $A_1,B_1,C_1$ are collinear.