General method of Complex Polynomial for determining the radius of the circle circumscribed to a cyclic polygon an arbitrary number of sides, and some important consequences

Abstract

This paper presents a general method for obtaining radius of the corresponding circumference to a cyclical polygon $n$ sides given the lengths of said sides, using the notion of complex number. As of radius $r$, obtained, can then be calculated polygon area in question applying known expressions which requires, after $n=4$, a powerful calculation tool. Are also given like elements regarding non convex polygons cyclic, although in this respect it deepens less and is not considered, course, the calculation of areas.