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Circle of antisimilitude

Index Circle of antisimilitude

In inversive geometry, the circle of antisimilitude (also known as mid-circle) of two circles, α and β, is a reference circle for which α and β are inverses of each other. [1]

11 relations: Angle, Circle, Congruence (geometry), David Eppstein, Degeneracy (mathematics), Inversive geometry, Isodynamic point, Limiting point (geometry), Radical axis, Reflection (mathematics), Reflection symmetry.

Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Circle

A circle is a simple closed shape.

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Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

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David Eppstein

David Arthur Eppstein (born 1963) is an American computer scientist and mathematician.

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Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

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Inversive geometry

In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.

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Isodynamic point

In Euclidean geometry, the isodynamic points of a triangle are points associated with the triangle, with the properties that an inversion centered at one of these points transforms the given triangle into an equilateral triangle, and that the distances from the isodynamic point to the triangle vertices are inversely proportional to the opposite side lengths of the triangle.

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Limiting point (geometry)

In geometry, the limiting points of two disjoint circles A and B in the Euclidean plane are points p that may be defined by any of the following equivalent properties.

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Radical axis

The radical axis (or power line) of two circles is the locus of points at which tangents drawn to both circles have the same length.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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Reflection symmetry

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.

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Redirects here:

Mid-circle, Midcircle.

References

[1] https://en.wikipedia.org/wiki/Circle_of_antisimilitude

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