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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,
eyeball theorem, red chords are of equal length theorem variation, blue chords are of equal length. The eyeball theorem is a statement in elementary geometry about a property of a pair of disjoined circles. More precisely it states the following: [1]
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 ]
In the geometry of numbers, Schinzel's theorem is the following statement: Schinzel's theorem — For any given positive integer n {\displaystyle n} , there exists a circle in the Euclidean plane that passes through exactly n {\displaystyle n} integer points.
Download QR code; Print/export Download as PDF; ... Pages in category "Theorems about circles" The following 21 pages are in this category, out of 21 total.
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)
The proofs of the Kronecker–Weber theorem by Kronecker (1853) and Weber (1886) both had gaps. The first complete proof was given by Hilbert in 1896. In 1879, Alfred Kempe published a purported proof of the four color theorem, whose validity as a proof was accepted for eleven years before it was refuted by Percy Heawood.
Miquel's theorem is a result in geometry, named after Auguste Miquel, [1] concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides.