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When circle () coincides with circle (), the Eight circles theorem degenerates into Brianchon's theorem [10]. When points = = = = = move to infinity, the dual of the Eight circles theorem becomes the Pascal's theorem. When applying the dual of the Eight circles theorem, with circle (A) being the circumcircle and circle (B) being the First ...
A variant of this theorem states that if one draws line in such a way that it intersects for the second time at ′ and at ′, then it turns out that | ′ | = | ′ |. [ 3 ] There are some proofs for Eyeball theorem, one of them show that this theorem is a consequence of the Japanese theorem for cyclic quadrilaterals .
Pages in category "Theorems about circles" The following 21 pages are in this category, out of 21 total. ... Code of Conduct; Developers; Statistics; Cookie statement;
Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem. Thales' theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy's theorem.
A short elementary proof of Pascal's theorem in the case of a circle was found by van Yzeren (1993), based on the proof in (Guggenheimer 1967). This proof proves the theorem for circle and then generalizes it to conics. A short elementary computational proof in the case of the real projective plane was found by Stefanovic (2010).
Five circles theorem ; Five color theorem (graph theory) Fixed-point theorems in infinite-dimensional spaces; Floquet's theorem (differential equations) Fluctuation dissipation theorem ; Fluctuation theorem (statistical mechanics) Ford's theorem (number theory) Focal subgroup theorem (abstract algebra) Folk theorem (game theory)
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 each tangent to its two neighbors, the three lines drawn between opposite pairs of the points of tangency on the seventh circle all pass through the same point.
The following proof is attributable [2] to Zacharias. [3] Denote the radius of circle by and its tangency point with the circle by . We will use the notation , for the centers of the circles. Note that from Pythagorean theorem,