Teorema de Casey : uma generalização do Teorema de Ptolomeu para quadriláteros inscritíveis

Abstract

This work shows in its main content a generalization of Ptolomy's Theorem first published in 1866 by John Casey, an Irish mathematician. This theorem denominated Casey's Theorem is being presented in this work with its detailed demonstrations, separated in two situations, with a lot of images to facilitate the reader's comprehension. It also presents a demonstration of Ptolomy's Theorem, several applications when solving some problems of Mathematics Olympiad, as well as some theorems, axioms and properties of Plane Euclidian Geometry, which are used in the demonstrations of the main theorems of this work.