2004 Cayley Problem 8

In the diagram, O is the centre of each circle. The circumferences of the circles are 24\pi and 14\pi. B is a point on the outer circle and OB intersects the inner circle at A. The length of AB is

\textbf{(A)}\ \sqrt{10}\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 7\quad \textbf{(D)}\ 10\pi\quad \textbf{(E)}\ 3

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.