# 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 ApolloniusCircle 2013-03-22 11:44:22 2013-03-22 11:44:22 drini (3) drini (3) 11 drini (3) Definition msc 51-00 msc 35-01 HarmonicDivision