VTMO 2026 - Grade 7 - Final - SET 10 - Self-study Question 5

In triangle $ABC$, $AB\lt AC$. Choose $E$ on the ray opposite to $BA$ with $BE=AC$, and $F$ on the ray opposite to $CA$ with $CF=AB$. Let $M$ be the midpoint of $BC$, $N=AM\cap EF$, and $D=NC\cap EM$.

a) Prove $MA=MN$.

b) Prove $AN=DF$.