On the circles of Apollonius associated with a triangle (Q1198229)
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scientific article; zbMATH DE number 92582
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the circles of Apollonius associated with a triangle |
scientific article; zbMATH DE number 92582 |
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On the circles of Apollonius associated with a triangle (English)
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16 January 1993
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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).
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Apollonius circles
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triangle
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0.91374564
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0.8829545
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0.8763641
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