Cyclic quadrilaterals

A quadrilateral is cyclic if and only if there exists a circle that passes through all four of its vertices. The most important property of cyclic quadrilaterals is that the sum of each pair of opposite angles is $180^\circ$.

Important properties

• The sum of the measures of opposite angles is $180^\circ$.

• A quadrilateral is cyclic if and only if its opposite angles are supplementary.

• Any triangle can be inscribed in a circle, but not every quadrilateral can.

• If a quadrilateral is cyclic, its exterior angle at a vertex equals the interior opposite angle.