2000 Cayley Problem 19

A metal rod with ends A and B is welded at its middle, C, to a cylindrical drum of diameter 12. The rod touches the ground at A making a 30° angle. The drum starts to roll along AD in the direction of D. How far along AD must the drum roll for B to touch the ground?

\textbf{(A)}\ \pi\quad \textbf{(B)}\ 2\pi\quad \textbf{(C)}\ 3\pi\quad \textbf{(D)}\ 4\pi\quad \textbf{(E)}\ 5\pi

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