Apollonius’ circle

Apollonius’ circle. The locus of a point moving so that the ratio of its distances from two fixed points is fixed, is a circle.

If two circles $C_1$ and $C_2$ are fixed with radii $r_1$ and $r_2$, then the circle of Apollonius of the two centers with ratio $r_1/r_2$ is the circle whose diameter is the segment that the two homothety centers of the circles.

Title	Apollonius’ circle
Canonical name	ApolloniusCircle
Date of creation	2013-03-22 11:44:22
Last modified on	2013-03-22 11:44:22
Owner	drini (3)
Last modified by	drini (3)
Numerical id	11
Author	drini (3)
Entry type	Definition
Classification	msc 51-00
Classification	msc 35-01
Related topic	HarmonicDivision