Question 6
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 $x + y \geq 2c$. (You may assume that $\tan \theta \geq \theta$ for $0 \leq \theta \lt \frac{\pi}{2}$.)