VTMO 2020 — Grade 8 — vtmo Question 17

$ABC$ is isosceles at $A , M$ midpoint $AB , F$ on $AC , E$ on the ray opposite $BA$. VI states $BE = CF$; EN states $BE = 2 CF$. Reflect A in $F$ to $D$, set $K = EF \cap BC , N = DK \cap AB$. Prove $MN = CF$.