Computations of the area and radius of cyclic polygons given by the lengths of sides

Abstract

Some properties of inscribed polygons, i.e., such plane polygons whose vertices lie on a circle, are investigated. Given an inscribed polygon with the lengths of its sides, we explore the area and radius of its circumcircle. We start with a triangle and a quadrangle and then we will explore the case of a pentagon. All the computations are based on results of commutative algebra especially on Gröbner bases method and elimination of variables in a given ideal. © Springer-Verlag Berlin Heidelberg 2006.