Three points $A$, $B$ and $C$ are on a circle, $G$. Suppose $\overline{AB}>\overline{AC}$. Let $M$ be the midpoint of the arc of the circle containing the points A and N the point in $AB$ such that $MN \perp AB$.
I would like to prove that $\overline{AC}=\overline{AN}+\overline{NB}$.