Definition
The Apollonian circles are defined in two different ways by a line segment denoted CD.
Each circle in the first family (the blue circles in the figure) is associated with a positive real number r, and is defined as the locus of points X such that the ratio of distances from X to C and to D equals r,
For values of r close to zero, the corresponding circle is close to C, while for values of r close to ∞, the corresponding circle is close to D; for the intermediate value r = 1, the circle degenerates to a line, the perpendicular bisector of CD. The equation defining these circles as a locus can be generalized to define the Fermat–Apollonius circles of larger sets of weighted points.
Each circle in the second family (the red circles in the figure) is associated with an angle θ, and is defined as the locus of points X such that the inscribed angle CXD equals θ,
Scanning θ from 0 to π generates the set of all circles passing through the two points C and D.
Read more about this topic: Apollonian Circles
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