US-TST 2011 Problem 1

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 $HQ/HR$ .

Proposed by Zuming Feng