Cyclic polygon

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:

$AC\cdot BD=AB\cdot CD+BC\cdot AD.\,$