Question 5
A ball bearing consists of two cylinders with the same axis and $n$ equal balls between them. The centers of all the balls are on the same plane perpendicular to the axis of the cylinders and each ball touches both cylinders and two adjacent balls. Let $r$ be the radius of the balls and let $R$ be the radius of the outer cylinder. Prove that $r/R \lt \frac{\pi}{n+\frac{\pi}{n}}$. (Grade 11.)