MathDB

points on boundary of convex polygon

Source: (Indian) RMO 2009 Problem 5

November 29, 2009

inequalitiesconicsellipsegeometrycircumcircleinductionfunction

Problem Statement

A convex polygon is such that the distance between any two vertices does not exceed

1

(i)

Prove that the distance between any two points on the boundary of the polygon does not exceed

1

(ii)

X

and

Y

are two distinct points inside the polygon, prove that there exists a point

Z

on the boundary of the polygon such that XZ \plus{} YZ\le1.