Suppose ABCD be a cyclic quadrilateral inscribed in a circle of radius R. Angles of the quadrilateral are given by A, B, C and D. then A + C = B + D = π

If sides are given that the angles of the quadrilateral can be obtained by using the formulae

cos B =

The area S of the quadrilateral is given by

s =

and sin B =

= and R = circum-radius of

Δ ABC= Also, in a cyclic quadrilateral, AC.BD

= AB.CD + BC.AD

On the basis of above passage, answer the following

questions:

(i) If a quadrilateral with side lengths a, b, c, d can be inscribed in one circle and circumscribed about another circle

then its area is-