Some extensions of a geometric inequality generated from Ptolemy’s inequality

2025/10/15 by Quang Hung Tran
Mathematics · #History and Theory of Mathematics #Mathematics and Applications

paper · doi:10.1017/mag.2025.10132

openalex created_date 2025/10/15 · openalex publication_date 2025/10/15 · crossref created 2025/10/15 · crossref issued 2025/11/01 · crossref published 2025/11/01 · crossref published-print 2025/11/01 · crossref published-online 2025/12/09 · openalex updated_date 2026/07/22 · crossref deposited 2026/07/27 · crossref indexed 2026/07/27

Abstract

For convenience, throughout this Article, we shall use the standard notations for any triangle ABC, where:1) the lengths of the sides BC, CA, AB are denoted by a, b, c, respectively,2) the area of the triangle is denoted by S,3) the semiperimeter of the triangle is denoted by s,4) the circumradius and inradius of the triangle are denoted by R and r, respectively,5) the lengths of the medians corresponding to vertices A, B, C are denoted by ma, mb, mc, respectively,6) the lengths of the angle bisectors corresponding to vertices A, B, C are denoted by la, lb, lc, respectively,7) the lengths of the altitudes corresponding to vertices A, B, C are denoted by ha, hb, hc, respectively.

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