(i)[4]
Find the combined area of the shaded regions in terms of $r$ and $\theta$.
(ii)[5]
For $\theta = \frac{1}{3}\pi$ and $r = 6$, find the total perimeter of the shaded regions, with your answer written in terms of $\sqrt{3}$ and $\pi$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
In the diagram, $OAB$ is an isosceles triangle with $OA = OB$ and angle $AOB = 2\theta$ radians. Arc $PST$ has centre $O$ and radius $r$, and line $ASB$ is tangent to arc $PST$ at $S$.