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Line parallel to base

Source: Sharygin Finals 2017, Problem 9.5

August 3, 2017
geometrySharygin Geometry Olympiadparallelaltitudesreflection

Problem Statement

Let BHb,CHcBH_b, CH_c be altitudes of an acute-angled triangle ABCABC. The line HbHcH_bH_c meets the circumcircle of ABCABC at points XX and YY. Points P,QP,Q are the reflections of X,YX,Y about AB,ACAB,AC respectively. Prove that PQ∥BCPQ \parallel BC.
Proposed by Pavel Kozhevnikov
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