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Conway's circle theorem as a special case of the generalisation, called "side divider theorem" (Villiers) or "windscreen wiper theorem" (Polster)) Conway's circle is a special case of a more general circle for a triangle that can be obtained as follows: Given any ABC with an arbitrary point P on line AB.
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 ]
Circle through exactly four points given by Schinzel's construction Schinzel proved this theorem by the following construction. If n {\displaystyle n} is an even number, with n = 2 k {\displaystyle n=2k} , then the circle given by the following equation passes through exactly n {\displaystyle n} points: [ 1 ] [ 2 ] ( x − 1 2 ) 2 + y 2 = 1 4 5 ...
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.
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]
Pascal's original note [1] has no proof, but there are various modern proofs of the theorem. It is sufficient to prove the theorem when the conic is a circle, because any (non-degenerate) conic can be reduced to a circle by a projective transformation. This was realised by Pascal, whose first lemma states the theorem for a circle.
Sion's minimax theorem (game theory) Sipser–Lautemann theorem (probabilistic complexity theory) (structural complexity theory) Siu's semicontinuity theorem (complex analysis) Six circles theorem ; Six exponentials theorem (transcendental number theory) Sklar's theorem ; Skoda–El Mir theorem (complex geometry)