Question 179
Let $ABC$ be an acute, non-isosceles triangle with circumcircle $(O)$. $BE$, $CF$ are the heights of $\triangle ABC$, and $BE$, $CF$ intersect at $H$. Let $M$ be the midpoint of $AH$, and $K$ be the point on $EF$ such that $HK$ is perpendicular to $EF$. A line not going through $A$ and parallel to $BC$ intersects the minor arcs $AB$ and $AC$ of $(O)$ at $P$, $Q$, respectively. Show that the tangent line of the circumcircle of $CQE$ at $E$, the tangent line of the circumcircle of $BPF$ at $F$, and $MK$ concur.