1998 Cayley Problem 22

A wheel of radius 8 rolls along the diameter of a semicircle of radius 25 until it bumps into this semicircle. What is the length of the portion of the diameter that cannot be touched by the wheel?

\textbf{(A)}\ 8\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 15\quad \textbf{(D)}\ 17\quad \textbf{(E)}\ 20

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.