Some properties of Kiepert lines of a triangle. Issue 547 (14th March 2016)

• Record Type: Journal Article
• Authors: Fox, Michael
• Is Part Of: Mathematical gazette. Volume 100:Issue 547(2016)
• Page Start: 54
• Page End: 67
• Publication Date: 2016-03-14
• 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.2016.8
• Languages: English
• ISSNs: 0025-5572

Abstract

Abstract : This article describes an investigation into Kiepert lines, and leads to some surprising and little-known relationships between the Fermat, Napoleon and Vecten points of a triangle. If we draw similar isosceles triangles A'BC, B'CA and C'AB outwards on the sides of a given scalene triangle ABC as in Figure 1, Kiepert's theorem tells us that the lines A'A, B'B and C'C meet in a single point - a Kiepert point [1, Chapter 11]. Since its position depends on the common base angles θ of the isosceles triangles, I label it K(θ), taking θ as the parameter of this point.