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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, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.
Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .
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.
Arithmetic Riemann–Roch theorem (algebraic geometry) BBD decomposition theorem (algebraic geometry) Base change theorems (algebraic geometry) Beauville–Laszlo theorem (vector bundles) Belyi's theorem (algebraic geometry) Bertini's theorem (algebraic geometry) Bézout's theorem (algebraic geometry) Borel fixed-point theorem (algebraic geometry)
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
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 circles defines a new circle by the second theorem. Then these six new circles C all pass through a single point. The sequence of theorems can be continued indefinitely.
In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
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