AMC 8 2016 Problem 25

A semicircle is inscribed in an isosceles triangle with base $16$ and height $15$ so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?

$\textbf{(A) }4 \sqrt{3} \textbf{(B) } \dfrac{120}{17} \textbf{(C) }10 \textbf{(D) }\dfrac{17\sqrt{2}}{2} \textbf{(E)} \dfrac{17\sqrt{3}}{2}$