Let $ABC$ be an acute-angled triangle. The external bisector of $\angle BAC$ meets the line $BC$ at point $N$. Let $M$ be the midpoint of $BC$. $P$ and $Q$ are two points on the line $AN$ such that $\angle PMN = \angle MQN = 90^\circ $. If $PN = 7$ and $BC=3$, then the length of $QA$ can be expressed as $\frac ab$, where $a$ and $b$ are coprime positive integers. What is the value of $(a+b)$?