# cyclic quadrilateral

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 $180^{\circ}$.

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