CAPS 2012 Problem 3

Let $ABCD$ be a cyclic quadrilateral with circumcircle $\omega$ . Let $I, J$ and $K$ be the incentres of the triangles $ABC, ACD$ and $ABD$ respectively. Let $E$ be the midpoint of the arc $DB$ of circle $\omega$ containing the point $A$ . The line $EK$ intersects again the circle $\omega$ at point $F$ $(F \neq E)$ . Prove that the points $C, F, I, J$ lie on a circle.