2021/05/08 by Ömer Avcı, Avcı, Ömer, Ömer Talip Akalın +5
Mathematics · Engineering · #Mathematics and Applications #graph theory and CDMA systems #Advanced Theoretical and Applied Studies in Material Sciences and Geometry
paper · pdf · doi:10.48550/arxiv.2105.03673
Apollonius of Perga, showed that for two given points A,B in the Euclidean plane and a positive real number k≠ 1, geometric locus of the points X that satisfies the equation |XA|=k|XB| is a circle. This circle is called Apollonius circle. In this paper we generalize the definition of the Apollonius circle for two given circles Γ1,Γ2 and we show that geometric locus of the points X with the ratio of the power with respect to the circles Γ1,Γ2 is constant, is also a circle. Using this we generalize the definition of Apollonius Circle, and generalize some results about Apollonius Circle.