coaxial circles | pencil of coaxal circles

Coaxal circles are circles whose centers are collinear and that share a common radical line. The collection of all coaxal circles is called a pencil of coaxal circles. It is possible to combine the two types of coaxal systems illustrated above such that the sets are orthogonal. Note that not all circles sharing the same radical line need be coaxal, since the lines of their centers need only be perpendicular to the radical line and therefore may not coincide. Members of a coaxal system satisfy x^2 + y^2 + 2λ x + c = (x + λ)^2 + y^2 + c - λ^2 = 0 for values of λ.

circle | coaxaloid system | Gauss-Bodenmiller theorem | limiting point | point circle | radical line