Question 96
In an acute triangle $ABC$, let $D$, $E$, and $F$ be the midpoints of sides $BC$, $CA$, and $AB$ respectively. Let $X$ and $Y$ be the feet of the perpendiculars drawn from $D$ to sides $AB$ and $AC$ respectively. The line passing through $F$ and parallel to line $XY$ intersects line $DY$ at a point $P$ that is different from $E$. Prove that line $AD$ and line $EP$ are perpendicular.