Pencil of circles

This term is related to: incidence geometry
View other terms related to incidence geometry | View facts related to incidence geometry

This term is related to: inversive geometry
View other terms related to inversive geometry | View facts related to inversive geometry

Definition

A pencil of circles in an inversive plane is a maximal collection of mutually tangent circles through a common point. The common point is termed the carrier of the pencil. By the axioms of inversive geometry, it turns out that for every point other than the common point, there is a unique member of the pencil through it.

A pencil of circles is also termed a parabolic pencil of circles.

Related notions

• Bundle of circles, also termed hyperbolic pencil of circles
• Flock of circles, also termed elliptic pencil of circles