1962 AHSME Problem 25

Given square ABCD with side 8 feet. A circle is drawn through vertices A and D and tangent to side BC. The radius of the circle, in feet, is:

\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 4 \sqrt{2} \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 5 \sqrt{2} \qquad \textbf{(E)}\ 6

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