CMO 1985 Problem 3

Let $P_1$ and $P_2$ be regular polygons of 1985 sides and perimeters $x$ and $y$ respectively. Each side of $P_1$ is tangent to a given circle of circumference $c$ and this circle passes through each vertex of $P_2$ . Prove $x + y \ge 2c$ . (You may assume that $\tan \theta \ge \theta$ for $0 \le \theta < \frac{\pi}{2}$ .)