SHARYGIN 2021 Problem 86

Let $ABC$ be an acute-angled triangle. Point $P$ is such that $AP = AB$ and $PB\parallel AC$ . Point $Q$ is such that $AQ = AC$ and $CQ\parallel AB$ . Segments $CP$ and $BQ$ meet at point $X$ . Prove that the circumcenter of triangle $ABC$ lies on the circle $(PXQ)$ .