AMO 2020 Problem 3

Let $ABC$ be a triangle with right angle at $\angle C$ . Suppose that the tangent line at C to the circle passing through $A,B,C$ intersects the line $AB$ at $D$ . Let $E$ be the midpoint of $CD$ and let $F$ be the point on the line $EB$ such that $AF$ is parallel to $CD$ . Prove that the lines $AB$ and $CF$ are perpendicular.