In the triangle $ABC$, $\angle{B} = 120^{\circ}$, point $M$ is the midpoint of side $AC$. On the sides $AB$ and $BC$, the points $K$ and $L$ are chosen such that $KL \parallel AC$. Prove that $MK + ML \geq MA$.
Source: 239 2008 S5
Tags: geometric inequality, inequalities
In the triangle $ABC$, $\angle{B} = 120^{\circ}$, point $M$ is the midpoint of side $AC$. On the sides $AB$ and $BC$, the points $K$ and $L$ are chosen such that $KL \parallel AC$. Prove that $MK + ML \geq MA$.