Triangles, Octagons, 11-gons and 16-gons [ILL 1974]
Source:
January 2, 2011
geometrycombinatorics proposedcombinatorics
Problem Statement
A regular octagon is given whose incircle has diameter . About is circumscribed a regular -gon, which is also inscribed in , cutting from eight isosceles triangles. To the octagon , three of these triangles are added so that exactly two of them are adjacent and no two of them are opposite to each other. Every -gon so obtained is said to be . Prove the following statement: Given a finite set of points lying in such that every two points of this set have a distance not exceeding , one of the -gons contains all of .