Cyclic Quadrilateral - Parameshvara's Formula

Parameshvara's Formula

A cyclic quadrilateral with successive sides a, b, c, d and semiperimeter s has the circumradius (the radius of the circumcircle) given by

This was derived by the Indian mathematician Vatasseri Parameshvara in the 15th century.

Using Brahmagupta's formula, Parameshvara's formula can be restated as

where K is the area of the cyclic quadrilateral.