Question 25
Let $ABCD$ be a convex cyclic quadrilateral and $M$ the midpoint of $[AC]$. The circumcircle of $CDM$ meets $(BC)$ a second time at $N$ (other than $C$). Let $B'$ be the reflection of $B$ in $N$. Show that $(MN)$ is tangent to the circumcircle of $B'DN$.