IR-TST 2016 Problem 17

Let $AD,BF,CE$ be altitudes of triangle $ABC$ . $Q$ is a point on $EF$ such that $QF=DE$ and $F$ is between $E,Q$ . $P$ is a point on $EF$ such that $EP=DF$ and $E$ is between $P,F$ .Perpendicular bisector of $DQ$ intersect with $AB$ at $X$ and perpendicular bisector of $DP$ intersect with $AC$ at $Y$ .Prove that midpoint of $BC$ lies on $XY$ .