Question 19
In an acute scalene triangle $ABC$, points $D$, $E$, $F$ lie on sides $BC$, $CA$, $AB$, respectively, such that $AD \perp BC$, $BE \perp CA$, $CF \perp AB$. Altitudes $AD$, $BE$, $CF$ meet at orthocenter $H$. Points $P$ and $Q$ lie on segment $EF$ such that $AP \perp EF$ and $HQ \perp EF$. Lines $DP$ and $QH$ intersect at point $R$. Compute $HQ/HR$.