Question 48
Let $ABCD$ be a quadrilateral with $\angle BAD = \angle ABC = 90^{\circ}$, and suppose $AB = BC = 1$, $AD = 2$. The circumcircle of $ABC$ meets $\overline{AD}$ and $\overline{BD}$ at points $E$ and $F$, respectively. If lines $AF$ and $CD$ meet at $K$, compute $EK$.