MathNet 2010 — Part 04 Question 136

They are $ABCD$ a cord quadrangle with the property that $\angle ABD = \angle DBC$. $E$ the intersection of the diagonals $AC$ and $BD$. $M$ the middle of $AE$ and $N$ the middle of $DC$. Prove that $MBCN$ is a cord quadrangle.