Question 62
In a non-isosceles acute triangle $ABC$, $D$ is the midpoint of the side $[BC]$. The points $E$ and $F$ lie on $[AC]$ and $[AB]$, respectively, and the circumcircles of $CDE$ and $AEF$ intersect at $P$ on $[AD]$. The bisector of the angle at $P$ in triangle $EFP$ intersects the line $EF$ at $Q$. Prove that the tangent line to the circumcircle of $AQP$ at $A$ is perpendicular to $BC$.