ÖMO 2014 Problem 6

Let $U$ be the center of the circumcircle of the acute-angled triangle $ABC$ . Let $M_A, M_B$ and $M_C$ be the circumcenters of triangles $UBC, UAC$ and $UAB$ respecrively. For which triangles $ABC$ is the triangle $M_AM_BM_C$ similar to the starting triangle (with a suitable order of the vertices)?