1973 AHSME Problem 9

In \triangle ABC with right angle at C, altitude CH and median CM trisect the right angle. If the area of \triangle CHM is K, then the area of \triangle ABC is

\textbf{(A)}\ 6K\qquad\textbf{(B)}\ 4\sqrt3\ K\qquad\textbf{(C)}\ 3\sqrt3\ K\qquad\textbf{(D)}\ 3K\qquad\textbf{(E)}\ 4K

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.