Question 14
Triangle $ABC$ is isosceles at $A$, and $M$ is the midpoint of $AB$. Take $F$ on $AC$ and $E$ on the ray opposite to $BA$ so that $BE=2CF$. Let $D$ be the reflection of $A$ across $F$. Lines $EF$ and $BC$ meet at $K$, and $DK$ meets $AB$ at $N$. Prove $MN=CF$.
