CEMC Gauss (Grade 8), 1999

In the diagram, $AC = CB = 10$ 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

(A) $12\pi$ (B) $6\pi$ (C) $3\pi$ (D) $2\pi$ (E) $0$