Concyclic Centroids and the Anti-Fuhrmann Triangle
| Autor: | K V, Sudharshan, Nene, Shantanu |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this article we present a remarkable concyclicity of four centroids related to the orthocenters of the triangles $ABC,$ $BPC,$ $CPA,$ and $PAB$ of a quadrangle $ABCP$. Furthermore, we establish a result about orthologic triangles inscribed in a rectangular hyperbola. We present an application of the concyclic centroids theorem when $P$ corresponds to the incenter $I$ of $ABC$. This specialization leads to the discovery of a novel triangle intimately connected to the Fuhrmann triangle. Comment: 10 pages, 4 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|