MathNet 2023-part-02 — 191 problems (EN–VI) Question 123

Let $AΒΓ$ be a triangle and $M$, $N$ the midpoints of $AB$, $AΓ$, respectively. The points $Δ$ and $E$ lie on the segment $BN$, such that $ΓΔ \parallel ME$ and $BΔ \lt BE$. Prove that:
$$
BΔ = 2 \cdot EN.
$$