SEAMO 2027 - Paper E - SET 05 - Self-study Question 14

Trapezoid $ABCD$ is inscribed in a circle with centre $O$, as shown. Given $AB\parallel CD$, $\angle COD=3\angle AOB$ and $AB/CD=2/5$, find $\dfrac{\operatorname{area}(\triangle BOC)}{\operatorname{area}(\triangle AOB)}$.