We are given a semicircle $k$ with center $O$ and diameter $AB$. Let $C$ be a point on $k$ such that $CO \bot AB$. The bisector of $\angle ABC$ intersects $k$ at point $D$. Let $E$ be a point on $AB$ such that $DE \bot AB$ and let $F$ be the midpoint of $CB$. Prove that the quadrilateral $EFCD$ is cyclic.