Inscribed n-gon and n-1-gon
Source: Baltic Way 1998
January 11, 2011
algebra proposedalgebra
Problem Statement
Let be an even integer. A regular -gon and a regular -gon are inscribed into the unit circle. For each vertex of the -gon consider the distance from this vertex to the nearest vertex of the -gon, measured along the circumference. Let be the sum of these distances. Prove that depends only on , and not on the relative position of the two polygons.