MathNet 2009-part-02 — 175 problems (EN–VI) Question 2

Let the triangle $ABC$ has barycenter $G$ and circumcenter $O$. The perpendicular bisectors of $GA$, $GB$ and $GC$ intersect at the points $A_1$, $B_1$, $C_1$. Prove that $O$ is the barycentre of the triangle $A_1B_1C_1$.