# cyclic quadrilateral

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 |