Eddy, R. H. An upper bound for a sequence of cevian inequalities. (English) Zbl 0604.51011 Elem. Math. 41, 128-130 (1986). 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. Reviewer: P.Smith Cited in 1 Review MSC: 51M05 Euclidean geometries (general) and generalizations 52A40 Inequalities and extremum problems involving convexity in convex geometry Keywords:cevian inequalities PDFBibTeX XMLCite \textit{R. H. Eddy}, Elem. Math. 41, 128--130 (1986; Zbl 0604.51011) Full Text: EuDML