1970 AHSME Problem 12

A circle with radius r is tangent to sides AB, AD, and CD of rectangle ABCD and passes through the midpoint of diagonal AC. The area of the rectangle in terms of r, is

\textbf{(A) }4r^2\qquad \textbf{(B) }6r^2\qquad \textbf{(C) }8r^2\qquad \textbf{(D) }12r^2\qquad \textbf{(E) }20r^2

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