MathDB
n-gons

Source: ToT - 2001 Fall Junior A-Level #2

August 17, 2011
geometryperimetergeometry unsolved

Problem Statement

Let n3n\ge3 be an integer. A circle is divided into 2n2n arcs by 2n2n points. Each arc has one of three possible lengths, and no two adjacent arcs have the same lengths. The 2n2n points are colored alternately red and blue. Prove that the nn-gon with red vertices and the nn-gon with blue vertices have the same perimeter and the same area.