Apollonian circle

An Apollonian circle is a special type of circle in geometry that relates to two given points, often called A and B. It represents all the points that maintain a constant ratio of distances to these two points. For example, if the ratio is 1:2, any point on this circle will be twice as far from point A as it is from point B. Apollonian circles help in solving problems involving distances, and they have applications in various fields, including mathematics, physics, and engineering. They are named after the ancient Greek mathematician Apollonius of Perga.