A Geometric Inequality for Convex Polygons

Abstract

Consider a regular polygon with vertices P1, P2, , Pn. Assume P is an interior point. Let [see pdf for notation] denote the Euclidean distance from P to Pi, i = 1, ...., n. Let A denote the area of the polygon. It is shown that [see pdf for notation] special cases of the above inequality are proved for some nonregular convex polygons. An example is given to show that the above inequality is not true for a general convex polygon.