Square A B C D has side length s, a circle centered at E has radius r, and r and s are both rational. The circle passes through D, and D lies on \overline{B E}. Point F lies on the circle, on the same side of \overline{B E} as A. Segment A F is tangent to the circle, and A F=\sqrt{9+5 \sqrt{2}}. What is r / s ?
Answer Choices
A. \dfrac{1}{2}
B. \dfrac{5}{9}
C. \dfrac{3}{5}
D. \dfrac{5}{3}
E. \dfrac{9}{5}