AMC 8 2013 Problem 23

Angle $ABC$ of $\triangle ABC$ is a right angle. The sides of $\triangle ABC$ are the diameters of semicircles as shown. The area of the semicircle on $\overline{AB}$ equals $8\pi$, and the arc of the semicircle on $\overline{AC}$ has length $8.5\pi$. What is the radius of the semicircle on $\overline{BC}$?

$\textbf{(A)}\ 7 \textbf{(B)}\ 7.5 \textbf{(C)}\ 8 \textbf{(D)}\ 8.5 \textbf{(E)}\ 9$