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...m]] and a square version of the [[Napoleon's theorem]]. All three of these theorems are just a special case of [[Petr–Douglas–Neumann theorem]]. ...cle]] and [[circumcircle]] of the triangle. Then construct two additional circles, each [[tangent]] to AM, BC, and to the circumcircle. Then their centers a ...

*Thales discovered the first theorems related to circles. ...

...es taken in pairs. Thus O coincides with the radical center of these three circles. * [[Seven circles theorem]] ...

'''Hadamard three-circle theorem''' is a result about the behavior of [[holomorphic function]]s. for any three [[concentric circles]] of radii <math>r_1<r_2<r_3.</math> ...

...vg|thumb|300px|Feuerbach's theorem: the [[nine-point circle]] is [[tangent circles|tangent]] to the [[incircle]] and [[excircles]] of a triangle. The incircle ...ncircle]] and [[nine-point circle]] of a triangle are internally [[tangent circles|tangent]] to each other at the '''Feuerbach point''' of the triangle. The F ...

[[Category:Theorems about triangles and circles]] ...

...the radii of the green circles is equal to the sum of the radii of the red circles * [[Tangent lines to circles]] ...

[[Image:Ford circles.svg|350px|right|thumb|[[Ford circle]]s.]] * {{Annotated link |Tangent lines to circles}} ...

== Related theorems == ...complicated closed-form formulas exist for the area of general polygons on circles, as described by Maley et al.<ref>{{cite journal |last1=Maley |first1=F. Mi ...

{{short description|Wooden tablets inscribed with geometrical theorems in Edo Japan}} ...tion tablet}}) are Japanese [[Euclidean geometry|geometrical]] problems or theorems on wooden tablets which were placed as offerings at [[Shinto shrine]]s or [ ...

...f distinguished circles (edge sets of [[simple cycle]]s), such that if two circles in the list are contained in a [[glossary of graph theory|theta graph]], th ...''''' is a '''linear class''' of circles; this by definition is a class of circles that satisfies the theta-graph property mentioned above. ...

...heorem]], showing that there is an infinity of triangles with the same two circles (and therefore the same ''R'', ''r'', and ''d'') ...the properties of triangles inscribed in and circumscribed about two given circles ...

...of the central angle subtended by the chord. See also [[Tangent lines to circles]]. ...As another example, the inscribed angle theorem is the basis for several theorems related to the [[power of a point]] with respect to a circle. Further, it a ...

[[Category:Theorems about quadrilaterals and circles]] ...

Most of the main theorems about [[covering space]]s, including the existence of a universal cover and the G ...

Points with equal power, [[isolines]] of <math>\Pi(P)</math>, are circles [[concentric]] to circle <math>c</math>. Steiner used the power of a point for proofs of several statements on circles, for example: ...

One of the most important theorems of complex analysis is that '''holomorphic functions are analytic and vice ...larger, since power series have no singularities in the interiors of their circles of convergence). ...

...iving works ''On the Moving Sphere'' and ''On Risings and Settings'', both about [[spherical geometry]]. ...[Little Astronomy]]",{{r|boyer}} a collection of miscellaneous short works about geometry and astronomy which were commonly transmitted together. They were ...

...ctedness]], which allows distinguishing a circle from two non-intersecting circles. ...aracteristic#Polyhedra|polyhedron formula]] are arguably the field's first theorems. The term ''topology'' was introduced by [[Johann Benedict Listing]] in the ...

...n planes), several theorems about the famous Steiner's chain of tangential circles, and a proof of the isoperimetric theorem (later a flaw was found in the pr ...and future generations. Eminent analysts succeeded in proving some of the theorems, but it was reserved to [[Luigi Cremona]] to prove them all, and that by a ...