Inequalities about the area bounded by three cevian lines of a triangle
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911251359072256 |
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| author | Aliyev, Yagub N. |
| author_facet | Aliyev, Yagub N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities about the area bounded by three cevian lines of a triangle Aliyev, Yagub N. Metric Geometry 51M16, 51M25, 51M04, 52A38, 52A40, 97G30, 97G40 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. |
| title | Inequalities about the area bounded by three cevian lines of a triangle |
| topic | Metric Geometry 51M16, 51M25, 51M04, 52A38, 52A40, 97G30, 97G40 |
| url | https://arxiv.org/abs/2401.00930 |