AMC 8 2017 Problem 22

In the right triangle $ABC$, $AC=12$, $BC=5$, and angle $C$ is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?

$\textbf{(A) }\frac{7}{6} \textbf{(B) }\frac{13}{5} \textbf{(C) }\frac{59}{18} \textbf{(D) }\frac{10}{3} \textbf{(E) }\frac{60}{13}$