New characterisations of bicentric quadrilaterals. Issue 567 (November 2022)

• Record Type: Journal Article
• Authors: Josefsson, Martin
• Is Part Of: Mathematical gazette. Volume 106:Issue 567(2022)
• Page Start: 414
• Page End: 426
• Publication Date: 2022-11
• Subjects: Mathematics -- Periodicals; Mathématique; Mathematik; Mathematics; Periodicals; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); Zeitschrift; Online-Publikation; 510
• DOI: 10.1017/mag.2022.114
• Languages: English
• ISSNs: 0025-5572

Abstract

Abstract : A bicentric quadrilateral is a convex quadrilateral that can have both an incircle (it is tangential) and a circumcircle (it is cyclic), see Figure 1. We know of only a dozen characterisations of bicentric quadrilaterals published before. In all of them the starting point is either a tangential or a cyclic quadrilateral, which then must satisfy some condition in order also to be of the other type. Before we proceed to prove seven new such necessary and sufficient conditions for bicentric quadrilaterals, we review one characterisation and one property of tangential quadrilaterals that we will apply later.