An upper bound for a sequence of cevian inequalities (Q1083694)
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scientific article; zbMATH DE number 3975768
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An upper bound for a sequence of cevian inequalities |
scientific article; zbMATH DE number 3975768 |
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An upper bound for a sequence of cevian inequalities (English)
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1986
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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.
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cevian inequalities
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