Problem

Source: Mathematics Regional Olympiad of Mexico Southeast 2015 P5

Tags: geometry, angle bisector, ratio



In the triangle $ABC$, let $AM$ and $CN$ internal bisectors, with $M$ in $BC$ and $N$ in $AB$. Prove that if $$\frac{\angle BNM}{\angle MNC}=\frac{\angle BMN}{\angle NMA}$$ then $ABC$ is isosceles.