CMOQR 2015 Problem 4

Given an acute-angled triangle $ABC$ whose altitudes from $B$ and $C$ intersect at $H$ , let $P$ be any point on side $BC$ and $X, Y$ be points on $AB, AC$ , respectively, such that $PB = PX$ and $PC = PY$ . Prove that the points $A, H, X, Y$ lie on a common circle.