Let $\displaystyle ABC$ be an triangle. On $\displaystyle AB$ side of the triangle let $\displaystyle D, E$ be two points so that $\displaystyle AD\leq AE$. Let $\displaystyle DF \parallel BC,F\in AC$ and $\displaystyle EG\parallel AC,G\in BC$. Let $\displaystyle L , M , N , P , R$ be the midpoints of the segments: $\displaystyle [CF] , [FD] , [DE] , [EG] , [GC]$. Proof that $\displaystyle [CN] , [PL] , [MR]$ can be the three sides of a triangle. Find a condition so that $\displaystyle MP\parallel AB$.