Triangle Trigonometry and Vectors · Superchallenge problem

Points $A$, $B$, $C$ lie on a circle of radius $1$ centred at $O$, and $3\,\overrightarrow{OA}+4\,\overrightarrow{OB}+5\,\overrightarrow{OC}=\mathbf{0}$. Find the area of $\triangle ABC$.