Question 78
The diagonals $AC$ and $BD$ of a convex quadrilateral $ABCD$ intersect at point $E$, $M$ is the midpoint of $AE$ and $N$ is the midpoint of $CD$. It is known that the diagonal $BD$ bisects $\angle ABC$. Prove that the quadrilateral $ABCD$ is cyclic if and only if the quadrilateral $MBCN$ is cyclic.