Question 17
Square $ABCD$ 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 $\overline{BE}.$ Point $F$ lies on the circle, on the same side of $\overline{BE}$ as $A.$ Segment $AF$ is tangent to the circle, and $AF = \sqrt{9 + 5\sqrt{2}}.$ What is $\frac{r}{s}?$
