Axis of Similitude of Three Circles

Given three non-intersecting circles C(xi, yi, ri), i = 1, 2, 3, that lie outside each other and have different radii, their centers of similitude are collinear, i.e., lie on a single straight line, known as the axis of similitude (or Monge Line) of the three circles. The line has the following equation

Ax - By = C,

where

A =
y1y2y3
r1r2r3
111
,   B =
x1x2x3
r1r2r3
111
,   C =
x1x2x3
y1y2y3
r1r2r3

References

  1. G. Salmon, Treatise on Conic Sections, Chelsea Pub, 6e, 1960, p. 107

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