PL-OM 1984 Problem 3

Let $W$ be a regular octahedron and $O$ be its center. In a plane $P$ containing $O$ circles $k_1(O,r_1)$ and $k_2(O,r_2)$ are chosen so that $k_1 \subset P\cap W \subset k_2$ . Prove that $\frac{r_1}{r_2}\le \frac{\sqrt3}{2}$