RO-TST 2012 Problem 7

Let $ABCD$ be a convex circumscribed quadrilateral such that $\angle ABC+\angle ADC<180^{\circ}$ and $\angle ABD+\angle ACB=\angle ACD+\angle ADB$ . Prove that one of the diagonals of quadrilateral $ABCD$ passes through the other diagonals midpoint.