Painting segments of a polygon Blue
Source: Tournament of Towns Spring 2015 Senior A-level
February 24, 2017
combinatoricscombinatorial geometry
Problem Statement
A convexgon with equal sides is located inside a circle. Each side is extended in both directions up to the intersection with the circle so that it contains two new segments outside the polygon. Prove that one can paint some of these new segments in red and the rest in blue so that the sum of lengths of all the red segments would be the same as for the blue ones.
( points)