CAPS 2013 Problem 1

Suppose $ABCD$ is a cyclic quadrilateral with $BC = CD$ . Let $\omega$ be the circle with center $C$ tangential to the side $BD$ . Let $I$ be the centre of the incircle of triangle $ABD$ . Prove that the straight line passing through $I$ , which is parallel to $AB$ , touches the circle $\omega$ .