In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the circle of antisimilitude (also known as mid-circle) of two circle

Circle

A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

s α and β is a circle for which α and β are inverses of each other. If α and β are non-intersecting or tangent, there exists one circle of antisimilitude; if α and β intersect at two points, there exist two circles of antisimilitude. When α and β are congruent

Congruence (geometry)

In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object...

, the circle of antisimilitude is degenerate

Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class....

; it becomes a line of symmetry, in which α and β are reflections

Reflection (mathematics)

In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as set of fixed points; this set is called the axis or plane of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection...

of each other.