Question 66
Given a right triangle $ABC$ ($\angle ACB = 90^\circ$), let $CH$, $H \in AB$, be the altitude to $AB$ and $P$ and $Q$ be the tangent points of the incircle of $\triangle ABC$ to $AC$ and $BC$, respectively. If $AQ \perp HP$ find the ratio $\frac{AH}{BH}$.