Question 48
Let $ABC$ be an acute triangle with $AB \lt AC$. Points $D, E$ lie on the interiors of $AB, AC$, respectively. Let $P$ be a point satisfying $PB = PD, PC = PE$. Let $X$ be a point on the interior of arc $AC$ of the circumcircle of $ABC$ which does not include the point $B$. The line $XA$ meets again the circumcircle of $ADE$ at $Y$. Show that $PX = PY$.