In triangle $ABC$ point $O$ is circumcenter. Point $T$ is centroid of $ABC$, and points $D$, $E$ and $F$ are circumcenters of triangles $TBC$, $TCA$ and $TAB$. Prove that $O$ is centroid of $DEF$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012
Tags: geometry, circumcircle