Question 193
Let $ABC$ be an acute, non-isosceles triangle with $AD$, $BE$, $CF$ as altitudes and $d$ is the tangent line of the circumcircle of triangle $ABC$ at $A$. The line through $H$ and parallel to $EF$ cuts $DE$, $DF$ at $Q$, $P$ respectively. Prove that $d$ is tangent to the ex-circle with respect to vertex $D$ of triangle $DPQ$.