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The formulas and properties given below are valid in the convex case. The word cyclic is from the Ancient Greek κύκλος (kuklos), which means "circle" or "wheel". All triangles have a circumcircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be cyclic is a non-square rhombus.
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.
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 ...
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 .
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. The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle subtending the same arc.
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 .
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.
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.
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