There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio 1:μ. 2. One of the eight circles that is simultaneously tangent to three given circles (i.e., a circle solving Apollonius' problem for three circles). 3. One of the three circles passing through a vertex and both isodynamic points S and S' of a triangle. 4. The circle that touches all three excircles of a triangle and encompasses them.
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