IOM 2018 Problem 2

A convex quadrilateral $ABCD$ is circumscribed about a circle $\omega$ . Let $PQ$ be the diameter of $\omega$ perpendicular to $AC$ . Suppose lines $BP$ and $DQ$ intersect at point $X$ , and lines $BQ$ and $DP$ intersect at point $Y$ . Show that the points $X$ and $Y$ lie on the line $AC$ .

Géza Kós