Question 35
Let $O$ be the center of a circle $k$. Points $A, B, C, D, E, F$ on $k$ are chosen such that the triangles $OAB$, $OCD$, $OEF$ are equilateral. Let $L, M, N$ be the midpoints of $BC$, $DE$, $FA$ respectively. Prove that triangle $LMN$ also is equilateral.