On the largest outscribed equilateral triangle. Issue 541 (March 2014)

• Record Type: Journal Article
• Authors: Dong, Fengming; Zhao, Dongsheng; Ho, Weng Kin
• Is Part Of: Mathematical gazette. Volume 98:Issue 541(2014)
• Page Start: 79
• Page End: 84
• Publication Date: 2014-03
• Subjects: Mathematics -- Periodicals; Mathématique; Mathematik; Mathematics; Periodicals; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); Zeitschrift; Online-Publikation; 510
• DOI: 10.1017/S0025557200000693
• Languages: English
• ISSNs: 0025-5572

Abstract

Abstract : Given two triangles Δ ABC and Δ DEF, if each side of Δ DEF contains a vertex of Δ ABC, then we call Δ DEF an outscribed triangle of Δ ABC . Given Δ ABC, let ΦΔ ABC be the set of all outscribed equilateral triangles of Δ ABC . Clearly ΦΔ ABC is non-empty. In the following we will determine the area of the largest member of ΦΔ ABC when each angle of Δ ABC is smaller than 120° and show that this largest member can be constructed by ruler and compass from Δ ABC . The corresponding problem on quadrilaterals has been considered in [1].