Question 131
Let $ABC$ be a triangle and $(I)$ the centre of its incircle. The line $(AI)$ meets $[BC]$ at $D$. The perpendicular bisector of $[AD]$ meets $(BI)$ at $M$ and $(CI)$ at $N$.
Show that $A$, $M$, $N$ and $I$ are concyclic.
Show that $A$, $M$, $N$ and $I$ are concyclic.