FI-MO 2018 Problem 3

The chords $AB$ and $CD$ of a circle intersect at $M$ , which is the midpoint of the chord $PQ$ . The points $X$ and $Y$ are the intersections of the segments $AD$ and $PQ$ , respectively, and $BC$ and $PQ$ , respectively. Show that $M$ is the midpoint of $XY$ .