Sharp bounds for cyclic sums of the ratio of the exradius to the sides of a triangle

DOI10.1186/s13660-015-0921-zzbMath1337.51009OpenAlexW2190660452WikidataQ59434838 ScholiaQ59434838MaRDI QIDQ896531

Yu-Ming Chu, Huan-Peng Yue, Shan-He Wu

Publication date: 9 December 2015

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-015-0921-z

zbMATH Keywords

triangleinequalitycircumradiusinradiussharp boundsexradiusratio-type

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Inequalities for trigonometric functions and polynomials (26D05) Inequalities and extremum problems in real or complex geometry (51M16)

Cites Work

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• A new refinement of the Janous-Gmeiner inequality for a triangle
• Geometric interpretation of Blundon's inequality and Ciamberlini's inequality
• An artificial proof of a geometric inequality in a triangle
• Some geometric inequalities involving angle bisectors and medians of a triangle
• A sharpened version of the fundamental triangle inequality
• General power inequalities between the sides and the circumscribed and inscribed radii related to the fundamental triangle inequality
• The best constant in a geometric inequality relating medians, inradius and circumradius in a triangle

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