3.26: Isosceles tangents outside a sector

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

The diagram shows the sector $OAB$ of a circle with centre $O$ and radius $20$. The perimeter of this sector is $65$. The lines $CA$ and $CB$ are both tangents to the circle at the points $A$ and $B$, so that the triangle $ABC$ is isosceles, with $AC = CB$. The angle $AOB$ is equal to $\theta$.

Find the area of the shaded region.