Problem

Source: Ukraine MO 2021 9.4

Tags: geometry, circumcircle



Let $ABC$ be a triangle with $\angle A = 60^\circ$. Points $P$ and $Q$ are chosen on sides $AB$ and $AC$, respectively, such that $BP = PQ = QC$. Prove that the circumcircle of $\triangle APQ$ passes through the projection of the orthocenter of $ABC$ onto its $A$-median. Proposed by Fedir Yudin