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The nine-point circles are all congruent with a radius of half that of the cyclic quadrilateral's circumcircle. The nine-point circles form a set of four Johnson circles. Consequently, the four nine-point centers are cyclic and lie on a circle congruent to the four nine-point circles that is centered at the anticenter of the cyclic quadrilateral.
Clausius theorem ; Clifford's circle theorems (Euclidean plane geometry) Clifford's theorem on special divisors (algebraic curves) Closed graph theorem (functional analysis) Closed range theorem (functional analysis) Cluster decomposition theorem (quantum field theory) Coase theorem ; Cochran's theorem
Pages in category "Theorems about circles" The following 21 pages are in this category, out of 21 total. This list may not reflect recent changes. B. Butterfly ...
Pages in category "Theorems about triangles and circles" The following 18 pages are in this category, out of 18 total. This list may not reflect recent changes. C.
The second theorem considers five circles in general position passing through a single point M. Each subset of four circles defines a new point P according to the first theorem. Then these five points all lie on a single circle C. The third theorem considers six circles in general position that pass through a single point M. Each subset of five ...
Pages in category "Theorems about quadrilaterals and circles" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. B.
In Euclidean plane geometry, Lester's theorem states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter lie on the same circle. The result is named after June Lester, who published it in 1997, [ 1 ] and the circle through these points was called the Lester circle by Clark Kimberling . [ 2 ]
The nine-point circle passes through these three midpoints; thus, it is the circumcircle of the medial triangle. These two circles meet in a single point, where they are tangent to each other. That point of tangency is the Feuerbach point of the triangle. Associated with the incircle of a triangle are three more circles, the excircles. These ...