Inequalities about the area bounded by three cevian lines of a triangle

2024/01/01 by Aliyev, Yagub N. · 1 citation
#51M04 #51M16 #51M25 #52A38 #52A40 #97G30 #97G40 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2401.00930

Abstract

In the paper we prove generalization of Schlömilch's and Zetel's theorems about concurrent lines in a triangle. This generalization is obtained as a corollary of sharp geometric inequality about the ratio of triangular areas which is proved using discrete variant of Hölder's inequality. Also a new sharp refinement of J.F. Rigby's inequality, which itself generalized Möbius theorem about the areas of triangles formed by cevians of a triangle, is proved.

Cited by

• The Maximum of the Volume of a Cevian Simplex and its Parts

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