Problem

Source: Stars of Mathematics 2018 seniors p4

Tags: convex polygon, disc, convex, diameter, geometric inequality, geometry



Given an integer $n \ge 3$, prove that the diameter of a convex $n$-gon (interior and boundary) containing a disc of radius $r$ is (strictly) greater than $r(1 + 1/ \cos( \pi /n))$. The Editors