2013 AMC8 Problem 23

#1
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 \(\overline{BC}\)?
23.png
\(\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 7.5 \qquad \textbf{(C)}\ 8 \qquad \textbf{(D)}\ 8.5 \qquad \textbf{(E)}\ 9\)