First Round, January 2019

Quadrilateral $ABCD$ has right angles at $A$ and $D$. A circle of radius $10$ fits neatly inside the quadrilateral and touches all four sides. The length of edge $BC$ is $24$. The midpoint of edge $AD$ is called $E$ and the midpoint of edge $BC$ is called $F$. What is the length of $EF$?

A) $\frac{43}{2}$ B) $\frac{13}{2}\sqrt{11}$ C) $\frac{33}{5}\sqrt{11}$ D) $22$ E) $\frac{45}{2}$