# Pencil of circles

From Groupprops

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*