TR-MO 2015 Problem 5

In a cyclic quadrilateral $ABCD$ whose largest interior angle is $D$ , lines $BC$ and $AD$ intersect at point $E$ , while lines $AB$ and $CD$ intersect at point $F$ . A point $P$ is taken in the interior of quadrilateral $ABCD$ for which $\angle EPD=\angle FPD=\angle BAD$ . $O$ is the circumcenter of quadrilateral $ABCD$ . Line $FO$ intersects the lines $AD$ , $EP$ , $BC$ at $X$ , $Q$ , $Y$ , respectively. If $\angle DQX = \angle CQY$ , show that $\angle AEB=90^\circ$ .