1998 Cayley Problem 20

Each side of square ABCD is 8. A circle is drawn through A and D so that it is tangent to BC. What is the radius of this circle?

\textbf{(A)}\ 4\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 4\sqrt{2}\quad \textbf{(E)}\ 5.25

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Full credit to this problem is given to the CEMC, you may view all Cayley contests here.