AHSME 1970 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 $\text{(A) } 4r^2 \text{(B) } 6r^2 \text{(C) } 8r^2 \text{(D) } 12r^2 \text{(E) } 20r^2$