On the circles of Apollonius associated with a triangle
type: Item
instance of: scholarly article
title: On the circles of Apollonius associated with a triangle
zbMATH Open document ID: 0757.51015
DOI: 10.1007/BF01228291
author: Ching-Kuang Shene
published in: Journal of Geometry
publication date: 1993-01-16T00:00:00Z
review text: The author provides short synthetic proofs for theorems on three circles of Apollonius that divide each of the sides of a given triangle in the ratios \(\alpha: \beta,\beta:\gamma\) and \(\alpha:\gamma\) respectively (\(\alpha > \beta > \gamma > 0\)) that were proven earlier [\textit{J. A. Hoskins}, \textit{W. D. Hoskins} and \textit{R. G. Stanton}, J. Geom. 38, No. 1/2, 52-58 (1990; Zbl 0714.51006)] analytically (using long algebraic computations).
Mathematics Subject Classification ID: 51M04
Mathematics Subject Classification ID: 51M15
zbMATH DE Number: 92582
zbMATH Keywords: Apollonius circles
zbMATH Keywords: triangle
reviewed by: Victor V. Pambuccian
MaRDI profile type: Publication
cites work: An optimal algorithm for constructing the weighted Voronoi diagram in the plane
cites work: A generalization of the circumcircle theorem
full work available at URL: https://doi.org/10.1007/bf01228291
OpenAlex ID: W2052730726
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description: scientific article; zbMATH DE number 92582