Question 162
Let $k$ be a semicircle with center $O$ and diameter $AB$. Let $C$ be a point on $k$ such that $CO \perp AB$. The bisector of $\angle ABC$ intersects $k$ at the point $D$. Let $E$ be the point of $AB$ such that $DE \perp AB$ and let $F$ be the midpoint of $CB$. Prove that the quadrilateral $EFCD$ is cyclic.