cyclic quadrilateral
Cyclic quadrilateral
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A quadrilateral is cyclic when its four vertices lie on a circle.
A necessary and sufficient condition for a quadrilateral to be cyclic, is that the sum of a pair of opposite angles be equal to 180∘.
One of the main results about these quadrilaterals is Ptolemy’s theorem.
Also, from all the quadrilaterals with given sides p,q,r,s, the one that is cyclic has the greatest area. If the four sides of a cyclic quadrilateral are known, the area can be found using Brahmagupta’s formula
| Title | cyclic quadrilateral |
| Canonical name | CyclicQuadrilateral |
| Date of creation | 2013-03-22 11:44:16 |
| Last modified on | 2013-03-22 11:44:16 |
| Owner | drini (3) |
| Last modified by | drini (3) |
| Numerical id | 12 |
| Author | drini (3) |
| Entry type | Definition |
| Classification | msc 51-00 |
| Classification | msc 81R50 |
| Classification | msc 81P05 |
| Classification | msc 81Q05 |
| Classification | msc 81-00 |
| Synonym | cyclic |
| Related topic | OrthicTriangle |
| Related topic | PtolemysTheorem |
| Related topic | ProofOfPtolemysTheorem |
| Related topic | Circumcircle |
| Related topic | Quadrilateral |