A

quadrilateral in which all four

vertices are

concyclic (lie on the same

circle). The following properties are found in every cyclic quadrilateral:

Opposite angles are Supplementary Angles (adding up to either 180 in degrees or pi in radians, depending on what you’re using).
Exterior angles are equal to the opposite interior angles.
When the diagonals are drawn, two pairs of similar triangles are formed.
The area can be determined by Brahmagupta's formula as well as Hero's formula as long as all sides are known.
Of all quadrilaterals with given four sides, the cyclic one is of greatest area.
The product of the two diagonals is equal to the sum of the products of opposite sides.