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In the special cases of one of the diagonals or sides being a diameter of the circle, this theorem gives rise directly to the angle sum and difference trigonometric identities. [17] The relationship follows most easily when the circle is constructed to have a diameter of length one, as shown here.
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.
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
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 ...
Haboush's theorem (algebraic groups, representation theory, invariant theory) Hadamard three-circle theorem (complex analysis) Hadamard three-lines theorem (complex analysis) Hadwiger's theorem (geometry, measure theory) Hahn decomposition theorem (measure theory) Hahn embedding theorem (ordered groups) Hairy ball theorem (algebraic topology)
As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle. As another example, the inscribed angle theorem is the basis for several theorems related to the power of a point with respect to a circle. Further, it allows one to prove ...
The second theorem considers five circles in general position passing through a single point M. Each subset of four circles defines a new point P according to the first theorem. Then these five points all lie on a single circle C. The third theorem considers six circles in general position that pass through a single point M. Each subset of five ...
The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
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