3.12: Sector data and shaded region beyond a tangent

In this question all lengths are in centimetres and all angles are in radians.

The diagram shows a circle with centre $O$ and radius $r$. The points $A$ and $B$ lie on the circumference of the circle such that the angle $AOB$ is $\theta$ and the length of the minor arc $AB$ is $12$. The area of the minor sector $AOB$ is $57.6\text{ cm}^{2}$. The point $C$ lies on the tangent to the circle at $A$ such that $OBC$ is a straight line.