BALKAN-SL 2008 G4

A triangle $ABC$ is given with barycentre $G$ and circumcentre $O$ . The perpendicular bisectors of $GA, GB$ meet at $C_1$ ,of $GB,GC$ meet at $A _1$ , and $GC,GA$ meet at $B_1$ . Prove that $O$ is the barycenter of the triangle $A_1B_1C_1$ .