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The Eight circles theorem and its dual can degenerate into Brianchon's theorem and Pascal's theorem when the conic in these theorems is a circle. Specifically: When circle () degenerates into a point, the Eight circles theorem degenerates into Brianchon's theorem [7] [9]. When circle () degenerates into a point and moves to infinity, the dual ...
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Clifford's circle theorems; Constant chord theorem; D.
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 .
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).
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. [1]
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)
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,
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.