CMO 2017 Problem 2

In acute triangle $ABC$ , let $\odot O$ be its circumcircle, $\odot I$ be its incircle. Tangents at $B,C$ to $\odot O$ meet at $L$ , $\odot I$ touches $BC$ at $D$ . $AY$ is perpendicular to $BC$ at $Y$ , $AO$ meets $BC$ at $X$ , and $OI$ meets $\odot O$ at $P,Q$ . Prove that $P,Q,X,Y$ are concyclic if and only if $A,D,L$ are collinear.