SMO 2013 Senior Round 1 Question 7

Question 7

$ABCD$ is a trapezium inscribed in a circle centred at $O$. It is given that $AB\parallel CD$, $\angle COD=3\angle AOB$, and $AB/CD=2/5$. Find the ratio

$$\frac{\text{area of }\triangle BOC}{\text{area of }\triangle AOB}.$$

Question illustration

$\frac32$
$\frac74$
$\frac{\sqrt3}{\sqrt2}$
$\frac{\sqrt5}2$
$\frac{\sqrt7}{\sqrt2}$