On Some Properties of a Complete Quadrangle

Abstract

In this paper, we study the properties of a complete quadrangle in the Euclidean plane. The proofs are based on using rectangular coordinates symmetrically on four vertices and four parameters a,b,c,d. Here, many properties of the complete quadrangle known from earlier research are proved using the same method, and some new results are given.

Isoptic Point of the Complete Quadrangle

“…There are many important points, lines, and circles related to the complete quadrangle, as introduced and proved in [1,2]. Here, we point out some of them that are important for further study in this paper.…”

“…In [1], we introduced the choice of a suitable coordinate system and placed a complete quadrangle in such a system. First, we will mention important definitions and statements proved in [1,2].…”

“…This is the fourth work in the series of such papers, and it considers the isoptic point of the complete quadrangle. In the second section, we provide an overview of the previously mentioned method and important points and circles, which were all introduced in previous papers [1][2][3]. In the third section, we present numerous results on the isoptic point of the complete quadrangle proved using our new method.…”

“…Our aim was to find a simple analytical tool with which it is possible to prove all of its properties using the same method. We have published several papers in this regard [1][2][3], where we present a unique method using rectangular coordinates that enables us to prove several properties of the complete quadrangle in a uniform way. This is the fourth work in the series of such papers, and it considers the isoptic point of the complete quadrangle.…”