NL-NWO 2013 Problem 3

The sides $BC$ and $AD$ of a quadrilateral $ABCD$ are parallel and the diagonals intersect in $O$ . For this quadrilateral $|CD| =|AO|$ and $|BC| = |OD|$ hold. Furthermore $CA$ is the angular bisector of angle $BCD$ . Determine the size of angle $ABC$ .

Attention: the figure is not drawn to scale.