# 2013 AMC8 Problem 23

#### bridge

##### Member
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 $$\overline{BC}$$?

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