Milorad Stevanović, The Apollonius circle and related triangle centers,
Forum Geometricorum 3 (2003) 187--195.

Abstract:  We give a simple construction of the Apollonius circle without directly invoking the excircles. This follows from a computation of the coordinates of the centers of similitude of the Apollonius circle with some basic circles associated with a triangle. We also find a circle  orthogonal to the five circles,  circumcircle, nine-point circle, excentral circle, radical circle of the excircles, and the Apollonius circle.

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