The excircle of a triangle $ABC$ corresponding to $A$ touches the side $BC$ at $M$, and the point on the incircle diametrically opposite to its point of tangency with $BC$ is denoted by $N$. Prove that $A,M,$ and $N$ are collinear.
Source: Moldova 2000 Grade 11 P3
Tags: geometry, Triangle
The excircle of a triangle $ABC$ corresponding to $A$ touches the side $BC$ at $M$, and the point on the incircle diametrically opposite to its point of tangency with $BC$ is denoted by $N$. Prove that $A,M,$ and $N$ are collinear.