On Ptolemy’s Theorem and Related Derivatives

Abstract

In this paper an Euclidean Geometric proof is presented for the Ptolemy’s Theorem of cyclic quadrilaterals by using a generalized identity with respect to a cevian of a triangle. Furthermore, a proof for the converse of the Ptolemy’s Theorem is also presented, while adducing some significant applications, new corollaries and lemmas of Ptolemy’s Theorem and its converse.