MathNet 2024-part-05 — 168 problems (EN–VI) Question 6

The sides $BC$, $CA$, $AB$ of the equilateral triangle $ABC$ contain the points $D$, $E$, respectively $F$, different from the sides' midpoints, so that $BD = CE = AF$. Denote $M$ the midpoint of $EF$ and $N$ the intersection of the lines $BC$ and $AM$. Prove that the segments $ND$ and $BC$ have the same midpoint.

Gheorghe Iurea