Question 78
Let $ABCD$ be a cyclic quadrilateral with $|AD|=|BD|$. Let $M=AC\cap BD$, let $I$ be the incenter of $\triangle BCM$, and let $N$ be the second intersection of $AC$ with the circumcircle of $\triangle BMI$. Prove that $|AN|\cdot|NC|=|CD|\cdot|BN|$.
