CGMO 2020 Problem 1

In the quadrilateral $ABCD$ , $AB=AD$ , $CB=CD$ , $\angle ABC =90^\circ$ . $E$ , $F$ are on $AB$ , $AD$ and $P$ , $Q$ are on $EF$ ( $P$ is between $E, Q$ ), satisfy $\frac{AE}{EP}=\frac{AF}{FQ}$ . $X, Y$ are on $CP, CQ$ that satisfy $BX \perp CP, DY \perp CQ$ . Prove that $X, P, Q, Y$ are concyclic.

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