1976 AHSME Problem 24

In the adjoining figure, circle K has diameter AB; circle L is tangent to circle K and to AB at the center of circle K; and circle M tangent to circle K, to circle L and AB. The ratio of the area of circle K to the area of circle M is \textbf{(A) }12\qquad \textbf{(B) }14\qquad \textbf{(C) }16\qquad \textbf{(D) }18\qquad \textbf{(E) }\text{not an integer}

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