BG-MO 1971 Problem 4

It is given a triangle $ABC$ . Let $R$ be the radius of the circumcircle of the triangle and $O_1,O_2,O_3$ be the centers of excircles of the triangle $ABC$ and $q$ is the perimeter of the triangle $O_1O_2O_3$ . Prove that $q\le6R\sqrt3$ . When does equality hold?