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Concyclic Centroids and the Anti-Fuhrmann Triangle

2023/12/04 by K, Sudharshan, Nene, Shantanu
#FOS: Mathematics #History and Overview (math.HO) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2312.02024

Abstract

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.

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