Question 13
On a circle with centre $O$, let $A$ and $B$ be points of the circle such that $AB = 120^\circ$ (that is, the arc $AB$ measures $120^\circ$). The point $C$ lies on the minor arc $AB$ and the point $D$ lies on the chord $AB$. It is known that $AD = 2$, $BD = 1$ and $CD = \sqrt{2}$. Compute the area of triangle $ABC$.