If a , b , c and d are the four sides of a bicentric quadrilateral then its area measures...
Pepe Chapuzas reasoned as follows:
Let s be the semiperimeter. Since the quadrilateral is circumscriptible...
a + c = b + d = s (Pitot's theorem)
Area = √ [(s−a)(s−b)(s−c)(s−d)] (Brahmagupta's formula)so
Area = √ (c·d·a·b)