Category:Circle of Apollonius

This category contains results about Circle of Apollonius.
Definitions specific to this category can be found in Definitions/Circle of Apollonius.

Let $A, B$ be distinct points in the plane.

Let $\lambda \in \R_{>0}$ be a strictly positive real number.

Let $X$ be the locus of points in the plane such that:

$X A = \map \lambda {X B}$

Then $X$ is a circle of Apollonius.