Apollonian circles

This article is about a family of circles sharing a radical axis, and the corresponding family of orthogonal circles. For other circles associated with Apollonius of Perga, see circles of Apollonius.
Some Apollonian circles. Every blue circle intersects every red circle at a right angle. Every red circle passes through the two points C, D, and every blue circle separates the two points.

In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned Greek geometer.