Chapter 6.4, Problem 37E

In $\odot O$, chord $\overline{AB}\parallel$ chord $\overline{CD}$. Radius $\overline{OE}$ is perpendicular to $\overline{AB}$ and $\overline{CD}$ at points $M$ and $N$, respectively. If $OE=13$, $AB=24$, and $CD=10$, then the distance from $O$ to $\overline{CD}$ is greater than the distance from $O$ to $\overline{AB}$. Determine how much farther chord $\overline{CD}$ is from center $O$ than chord $\overline{AB}$ is from center $O$; that is, find $MN$.