IMO 2002 Problem 2

The circle $S$ has centre $O$ , and $BC$ is a diameter of $S$ . Let $A$ be a point of $S$ such that $\angle AOB<120{{}^\circ}$ . Let $D$ be the midpoint of the arc $AB$ which does not contain $C$ . The line through $O$ parallel to $DA$ meets the line $AC$ at $I$ . The perpendicular bisector of $OA$ meets $S$ at $E$ and at $F$ . Prove that $I$ is the incentre of the triangle $CEF.$ Attachments: