Question 15
Let $ABC$ be a triangle inscribed in a circle. Let $M$ be the midpoint of the arc $AB$ that does not contain $C$ and $N$ be the midpoint of the arc $AC$ that does not contain $B$.
Let $E$ and $F$ be the points where the line $MN$ cuts the sides $AB$ and $AC$ respectively.
Prove that if $ME = EF = FN$, then the triangle $ABC$ is equilateral.
Let $E$ and $F$ be the points where the line $MN$ cuts the sides $AB$ and $AC$ respectively.
Prove that if $ME = EF = FN$, then the triangle $ABC$ is equilateral.