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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.
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 ...
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]
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.
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems , and play an important role in many geometrical constructions and proofs .
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. His second lemma states that what is true in one plane remains true upon projection to another plane. [1]
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who published it ...
Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.
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