# Cyclic polygon

From Citizendium

In plane geometry, a **cyclic polygon** is a polygon whose vertices all lie on one circle. The centre of the circle is the circumcentre of the polygon.

Every triangle is cyclic, since any three (non-collinear) points lie on a unique circle.

## Cyclic qusdrilateral

A **cyclic quadrilateral** is a quadrilateral whose four vertices are concyclic. A quadrilateral is cyclic if and only if pairs of opposite angles are supplementary (add up to 180°, π radians). **Ptolemy's theorem** states that in a cyclic quadrilateral *ABCD*, the product of the diagonals is equal to the sum of the two products of the opposite sides: