MathNet 2013 Question 48

Let ABCD be a convex cyclic quadrilateral with |AD|=|BD|. Its diagonals AC and BD meet at E. Let I be the incenter of triangle BCE. The circumcircle of triangle BIE meets the interior of segment AE at N. Prove that
$$|AN|\cdot|NC|=|CD|\cdot|BN|.$$