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The reflections of the vertices and the intersections of circumcircle with HaHb

Source: VI Caucasus Mathematical Olympiad

March 14, 2021
geometrygeometric transformationreflectioncircumcircle

Problem Statement

In an acute triangle ABCABC let AHaAH_a and BHbBH_b be altitudes. Let HaHbH_aH_b intersect the circumcircle of ABCABC at PP and QQ. Let A′A' be the reflection of AA in BCBC, and let B′B' be the reflection of BB in CACA. Prove that A′,B′A', B', PP, QQ are concyclic.
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