Category: Theorems about circles

Pizza theorem
In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because it mimics a traditional pizza slicin
Casey's theorem
In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey.
Intersecting secants theorem
The intersecting secant theorem or just secant theorem describes the relation of line segments created by two intersecting secants and the associated circle. For two lines AD and BC that intersect eac
Pestov–Ionin theorem
The Pestov–Ionin theorem in the differential geometry of plane curves states that every simple closed curve of curvature at most one encloses a unit disk.
Six circles theorem
In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent to two sides of the triangle and also to the preceding circle in the c
Butterfly theorem
The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows: Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn;
Circle packing theorem
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a
Tangent-secant theorem
The tangent-secant theorem describes the relation of line segments created by a secant and a tangent line with the associated circle. This result is found as Proposition 36 in Book 3 of Euclid's Eleme
Inscribed angle theorem
No description available.
Intersecting chords theorem
The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle.
Descartes' theorem
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can const
Monge's theorem
In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the thre
Bundle theorem
In Euclidean geometry, the bundle theorem is a statement about six circles and eight points in the Euclidean plane. In general incidence geometry, it is a similar property that a Möbius plane may or m
Inscribed angle
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two g
Seven circles theorem
In geometry, the seven circles theorem is a theorem about a certain arrangement of seven circles in the Euclidean plane. Specifically, given a chain of six circles all tangent to a seventh circle and
Five circles theorem
In geometry, the five circles theorem states that, given five circles centered on a common sixth circle and intersecting each other chainwise on the same circle, the lines joining their second interse
Clifford's circle theorems
In geometry, Clifford's theorems, named after the English geometer William Kingdon Clifford, are a sequence of theorems relating to intersections of circles.
Schinzel's theorem
In the geometry of numbers, Schinzel's theorem is the following statement: Schinzel's theorem — For any given positive integer , there exists a circle in the Euclidean plane that passes through exactl
Eyeball theorem
The eyeball theorem is a statement in elementary geometry about a property of a pair of disjoined circles. More precisely it states the following: For two nonintersecting circles and centered at and t
Constant chord theorem
The constant chord theorem is a statement in elementary geometry about a property of certain chords in two intersecting circles. The circles and intersect in the points and . is an arbitrary point on