IR-TST 2017 Problem 5

In triangle $ABC$ , arbitrary points $P,Q$ lie on side $BC$ such that $BP=CQ$ and $P$ lies between $B,Q$ .The circumcircle of triangle $APQ$ intersects sides $AB,AC$ at $E,F$ respectively.The point $T$ is the intersection of $EP,FQ$ .Two lines passing through the midpoint of $BC$ and parallel to $AB$ and $AC$ , intersect $EP$ and $FQ$ at points $X,Y$ respectively. Prove that the circumcircle of triangle $TXY$ and triangle $APQ$ are tangent to each other.

Proposed by Iman Maghsoudi