MathDB

convex polygon with 4n+2 sides

Source: Romanian IMO TST 2005 - day 2, problem 1

April 1, 2005

geometrygeometry proposed

Problem Statement

Prove that in any convex polygon with

4n+2

sides (

n\geq 1

) there exist two consecutive sides which form a triangle of area at most

\frac 1{6n}

of the area of the polygon.