AHSME 1967 Problem 32

In quadrilateral $ABCD$ with diagonals $AC$ and $BD$, intersecting at $O$, $BO=4$, $OD = 6$, $AO=8$, $OC=3$, and $AB=6$. The length of $AD$ is: $\textbf{(A)}\ 9 \textbf{(B)}\ 10 \textbf{(C)}\ 6\sqrt{3} \textbf{(D)}\ 8\sqrt{2} \textbf{(E)}\ \sqrt{166}$