examday

/TMUA

Points $A$ and $B$ lie on a circle with centre $O$ and radius $r$. The line segment $AB$ is a diameter of the circle. Point $C$ lies on the circumference of the circle such that the angle $CAB$ is $30^\circ$. A tangent to the circle at $C$ intersects $AB$ extended at a point $D$, with $B$ between $A$ and $D$.

Let $S_1$ be the area of triangle $ABC$ and $S_2$ be the area of triangle $OCD$. Which of the following statements is true?