Regular n-gon E can be joined by two circular arcs
Source: IMO Shortlist 1989, Problem 7, ILL 16
September 18, 2008
geometryanglegeometric inequalitypolygonIMO Shortlist
Problem Statement
Show that any two points lying inside a regular n\minus{}gon can be joined by two circular arcs lying inside and meeting at an angle of at least \left(1 \minus{} \frac{2}{n} \right) \cdot \pi.