Question 22
Let $H$ denote the intersection of the altitudes $AD$ and $CE$ of an acute triangle $ABC$. Let $M$ and $N$ denote the midpoints of the sides $AB$ and $BC$ respectively. The rays $MH$ and $NH$ intersect the circumcircle $\omega$ of $ABC$ at points $K$ and $L$ respectively. If the circumcircles of the triangles $EHK$ and $DHL$ intersect $\omega$ again at $P$ and $Q$, show that the points $D, E, P, Q$ lie on a common circle.
(Batzaya G.)
(Batzaya G.)