On the circles of Apollonius associated with a triangle
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).
scientific article; zbMATH DE number 92582