Inequalities about the area bounded by three cevian lines of a triangle
Metric Geometry
2025-11-07 v2
Abstract
In the paper we prove generalization of Schl\"omilch'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 H\"older's inequality. Also a new sharp refinement of J.F. Rigby's inequality, which itself generalized M\"obius theorem about the areas of triangles formed by cevians of a triangle, is proved.
Keywords
Cite
@article{arxiv.2401.00930,
title = {Inequalities about the area bounded by three cevian lines of a triangle},
author = {Yagub N. Aliyev},
journal= {arXiv preprint arXiv:2401.00930},
year = {2025}
}