# 2006 iTest Problems/Problem U8

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## Problem

Let $T = TNFTPP$, and let $S$ be the sum of the digits of $T$. Cyclic quadrilateral $ABCD$ has side lengths $AB = 5$, $BC = 2$, $CD = 3$, 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 $m + n$.