2006 iTest Problems/Problem U8

Problem

Cyclic quadrilateral $ABCD$ has side lengths $AB  =  9$, $BC  =  2$, $CD  =  3$, and $DA  =  10$. Let $M$ and $N$ be the midpoints of sides $AD$ and $BC$. The diagonals $AC$ and $BD$ intersect $MN$ at $P$ and $Q$ respectively. $\frac{PQ}{MN}$ can be expressed as $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Determine $m  +  n$.