Axis of Similitude of Three Circles
Given three nonintersecting circles C(x_{i}, y_{i}, r_{i}), 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 = 
 ,  B = 
 ,  C = 

References
 G. Salmon, Treatise on Conic Sections, Chelsea Pub, 6e, 1960, p. 107
Contact Front page Contents Geometry
Copyright © 19962018 Alexander Bogomolny71927470