Inequalities about the area bounded by three cevian lines of a triangle
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2024
- DOI:
- 10.48550/arXiv.2401.00930
- arXiv:
- arXiv:2401.00930
- Bibcode:
- 2024arXiv240100930A
- Keywords:
-
- Mathematics - Metric Geometry;
- 51M16;
- 51M25;
- 51M04;
- 52A38;
- 52A40;
- 97G30;
- 97G40
- E-Print:
- Elemente der Mathematik 2024