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 joins the two homothety centers of the circles.