Question 134
The side $AB$ is the least side in a triangle $ABC$. Points $M$ and $N$ are marked on the rays $CA$ and $CB$ respectively so that $CM = MB$, $CN = NA$. Let $O$ be a circumcenter of the triangle $ABC$.
Prove that $A$, $B$, $N$, $M$, and $O$ are concyclic.
Prove that $A$, $B$, $N$, $M$, and $O$ are concyclic.