AN APPLICATION OF ELEMENTS OF THE QUADRILATERAL’S GEOMETRY FOR SOLVING NON-STANDARD PROBLEMS

Abstract

Lately, the foundations of a complete geometry of the quadrilateral were laid, built in analogy of the classical geometry of the triangle. Several articles were devoted to it, the PhD-dissertation work of one of the authors of this article (Stefanov, St. 2020), and a book encompassing it in its entirety is soon to be published. This publication aims to convince the readers in the benefits of studying this geometry. During the last years the rubrics „Contest problems“ and „Problems М+“ of the journals „Mathematics and Informatics“ and „Mathematics Plus“ included difficult problems, whose solutions are complex for somebody who doesn't know and doesn't use elements of the quadrilateral’s geometry. Knowing the properties of the remarkable points, lines and circles, as well as the mappings in the quadrilateral, which are subjects of its geometry, not only provides ideas for solving this problem, but also serves for their implementation (to carry out the solution). This was shown once in (Nenkov, Stefanov & Haimov 2020). We will confirm it here again, with new interesting examples.