Question 3
Let $ABC$ be an acute scalene triangle inscribed in circle $(O)$. The altitudes $BE,CF$ meet at the orthocenter $H$, and $M$ is the midpoint of $AH$. Let $K$ be the orthogonal projection of $H$ onto $EF$. A line not passing through $A$ and parallel to $BC$ meets the minor arcs $AB,AC$ at $P,Q$, respectively. Prove that the tangent at $E$ to the circumcircle of triangle $CQE$ and the tangent at $F$ to the circumcircle of triangle $BPF$ meet at a point on line $MK$.