Circles of Apollonius
![Figure 1. Apollonius' definition of a circle.](/Images/godic/202501/04/Apollonius_circle_definition_labels.svg5650.png")
![Figure 2. A set of Apollonian circles. Every blue circle intersects every red circle at a right angle, and vice versa. Every red circle passes through the two foci, which correspond to points A and B in Figure 1.](/Images/godic/202501/04/Apollonian_circles.svg5650.png")
![Apollonius' problem may have up to eight solutions. The three given circles are shown in black, whereas the solution circles are colored.](/Images/godic/202501/04/Apollonius8ColorMultiplyV2.svg5650.png")
![Figure 4. A symmetrical Apollonian gasket, also called the Leibniz packing, after its inventor Gottfried Leibniz.](/Images/godic/202501/04/Apollonian_gasket.svg5650.png")
The circle of Apollonius is any of several types of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection.