OMA 2008 Problem 3

On a circle of center $O$ , let $A$ and $B$ be points on the circle such that $\angle AOB = 120^o$ . Point $C$ lies on the small arc $AB$ and point $D$ lies on the segment $AB$ . Let also $AD = 2, BD = 1$ and $CD = \sqrt2$ . Calculate the area of triangle $ABC$ .