HMMT 2015 G3

Let $A B C D$ be a quadrilateral with $\angle B A D=\angle A B C=90^{\circ}$, and suppose $A B=B C=1, A D=2$. The circumcircle of $A B C$ meets $\overline{A D}$ and $\overline{B D}$ at points $E$ and $F$, respectively. If lines $A F$ and $C D$ meet at $K$, compute $E K$.