MathNet 2010 — Part 04 Question 111

Let $M$ and $N$ be points on the side $BC$ of the triangle $ABC$. It is known that $\angle BAM = \angle CAN$ and $AL$ is bisector of the angle $A$. Prove that $\frac{BM}{MC} + \frac{NB}{NC} \ge 2 \cdot \frac{BL}{LC}$.