Cyclic quadrilateral
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In geometry, a cyclic quadrilateral is a quadrilateral whose vertices are all lie on a single circle. The vertices are said to be concyclic.
- Opposite angles are supplementary angles (adding up to either 180 in degrees or π in radians).
- The area of a cyclic quadrilateral is given by Brahmagupta's formula as well as Heron's formula as long as the sides are given.
- The area of a cyclic quadrilateral is maximal among all quadrilaterals having the same side lengths.
- Exterior angles are equal to the opposite interior angles.
- When the diagonals are drawn, two pairs of similar triangles are formed.
- The product of the two diagonals is equal to the sum of the products of opposite sides. (Ptolemy's Theorem)
See also: cyclic polygon.
External links
- Cyclic quadrilateral theorem (http://agutie.homestead.com/files/sangaku2.html) by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas".
- Incenters in Cyclic Quadrilateral (http://www.cut-the-knot.org/Curriculum/Geometry/CyclicQuadrilateral.shtml)
- Four Concurrent Lines in a Cyclic Quadrilateral (http://www.cut-the-knot.org/Curriculum/Geometry/Brahmagupta2.shtml)de:Sehnenviereck