jmc

If the semicircle on $\overline{AB}$ were a full circle, the area would be $16\pi$. $\pi r^2=16\pi \Rightarrow r^2=16\Rightarrow r=+4$, therefore the diameter of the first circle is $8$. The arc of the largest semicircle is $8.5\pi$, so if it were a full circle, the circumference would be $17\pi$. So the $\text{diameter}=17$. y the Pythagorean theorem, the other side has length $15$, so the radius is $\boxed{7.5}$