Question 83
Point $M$ is the midpoint of side $BC$ of triangle $ABC$. The line perpendicular to $AM$ at point $A$ intersects the circumcircle of $ABC$ for the second time at $K$. The altitudes $BE$ and $CF$ of triangle $ABC$ intersect line $AK$ at points $P$ and $Q$, respectively. Prove that the radical axis of the circumcircles of $PKE$ and $QKF$ are perpendicular to $BC$.