CGMO 2014 Problem 6

In acute triangle $ABC$ , $AB > AC$ . $D$ and $E$ are the midpoints of $AB$ , $AC$ respectively. The circumcircle of $ADE$ intersects the circumcircle of $BCE$ again at $P$ . The circumcircle of $ADE$ intersects the circumcircle $BCD$ again at $Q$ . Prove that $AP = AQ$ .