# Cyclic quadrilateral (sine of an angle)

## Description

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. A convex quadrilateral ABCD is cyclic if and only if its opposite angles are supplementary. The sine of an angle of the quadrilateral can be calculated by the sides and the semiperimeter of the quadrilateral.

Related formulas## Variables

A | Angle of the quadrilateral between sides AB and AD (degrees) |

s | Semiperimeter of the cyclic quadrilateral (m) |

a | Length of the side of the cyclic quadrilateral (AB) (m) |

b | Length of the side of the cyclic quadrilateral (BC) (m) |

c | Length of the side of the cyclic quadrilateral (CD) (m) |

d | Length of the side of the cyclic quadrilateral (DA) (m) |