Answer: B

Video solution:

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Written solution:

The semicircle on $\overline{AB}$ has area $8\pi$, so its full circle would have area $16\pi$. Its radius is therefore $4$, and $AB=8$.

A semicircle of radius $r$ has arc length $\pi r$. Since the arc on $\overline{AC}$ has length $8.5\pi$, its radius is $8.5$, so $AC=17$.

Using the Pythagorean theorem in right triangle $ABC$, $$BC=\sqrt{17^2-8^2}=\sqrt{225}=15.$$ The radius of the semicircle on $\overline{BC}$ is $15/2=7.5$.

Thus, B is the correct answer.