1999 Gauss 8 Problem 22

In the diagram, AC = CB = 10\text{ m}, where AC and CB are each the diameter of the small equal semi-circles. The diameter of the larger semi-circle is AB. In travelling from A to B, it is possible to take one of two paths. One path goes along the semi-circular arc from A to B. A second path goes along the semi-circular arcs from A to C and then along the semi-circular arc from C to B. The difference in the lengths of these two paths is

\textbf{(A)}\ 12\pi\quad \textbf{(B)}\ 6\pi\quad \textbf{(C)}\ 3\pi\quad \textbf{(D)}\ 2\pi\quad \textbf{(E)}\ 0

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 Gauss contests here.