Problem

The diagram shows a sector of a circle with centre $C$. The radii $CA$ and $CB$ each have length $r$ cm and the size of the reflex angle $ACB$ is $\theta$ radians. The sector, shaded in the diagram, has a perimeter of $65$ cm and an area of $225 \text{ cm}^2$.

(a) Find the values of $r$ and $\theta$.

(b) Find the area of triangle $ACB$.