Show that any two points lying inside a regular $ n-$gon $ E$ can be joined by two circular arcs lying inside $ E$ and meeting at an angle of at least $ \left(1 - \frac{2}{n} \right) \cdot \pi.$
Problem
Source: IMO Shortlist 1989, Problem 7, ILL 16
Tags: geometry, angle, geometric inequality, polygon, IMO Shortlist