Question 95
Let $ABCD$ be a cyclic quadrilateral such that $|AD| = |BD|$ and let $M$ be the intersection of its diagonals. Let $N$ be the second intersection of the diagonal $AC$ with the circle passing through $B$, $M$ and the incentre of the triangle $BCM$. Prove that $|AN| \cdot |NC| = |CD| \cdot |BN|$.