An upper bound for a sequence of cevian inequalities
type: Item
instance of: scholarly article
title: An upper bound for a sequence of cevian inequalities
zbMATH Open document ID: 0604.51011
published in: Elemente der Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141388
review text: The altitudes, Gergonne cevians, internal angle bisectors, medians and Nagel cevians of a triangle satisfy the sequence of inequalities \(\Sigma h_ a\leq \Sigma g_ a\leq \Sigma w_ a\leq \Sigma m_ a\leq \Sigma n_ a.\) The author shows that \(\Sigma n_ a\leq 14R-19r,\) where R and r are respectively the circumradius and inradius of the triangle, with equality throughout the sequence when the triangle is equilateral.
Mathematics Subject Classification ID: 51M05
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 3975768
zbMATH Keywords: cevian inequalities
author: Roland H. Eddy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3975768