AHSME 1962 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: $\textbf{(A)}\ 4 \textbf{(B)}\ 4\sqrt{2} \textbf{(C)}\ 5 \textbf{(D)}\ 5\sqrt{2} \textbf{(E)}\ 6$