Question 59
Let $M$ and $N$ be, respectively, the feet of the altitudes from vertices $A$ and $B$ of the acute triangle $ABC$. Let $Q$ be the midpoint of the segment $\overline{MN}$ and let $P$ be the midpoint of the segment $\overline{AB}$. If $|MN| = 10$ and $|AB| = 26$, determine the length of the segment $\overline{PQ}$.