2003 Fermat Problem 17

In the diagram, \triangle ABC is right-angled at C. If BD = 2x, DC = x, and \angle ADC = 2(\angle ABC), then the length of AB is

\textbf{(A)}\ 2\sqrt{2}x\quad \textbf{(B)}\ \sqrt{6}x\quad \textbf{(C)}\ 2\sqrt{3}x\quad \textbf{(D)}\ 3x\quad \textbf{(E)}\ 4x

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 Fermat contests here.