Question 148
In triangle $ABC$ with orthocenter $H$, $AB = 13$, $BC = 21$ and $CA = 20$. The perpendicular bisector of $CH$ meets $BC$ at $P$ and lines $PH$ and $AB$ meet at $Q$. The line through $Q$ perpendicular to $PQ$ meets $AH$ at $X$. The length of $AX$ can be written in the form $p/q$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.