(a(i))[1]
Determine $AC$ in terms of $r$ and $\theta$.
(a(ii))[6]
Calculate the perimeter of the shaded region $ABD$ when $\theta = \frac{1}{3}\pi$ and $r = 4$, giving your answer exactly.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts the sector $OAB$ of a circle whose centre is $O$ and whose radius is $r$. The angle $AOB$ is $\theta$ radians. Point $C$ lies on $OA$ so that $BC$ is perpendicular to $OA$. Point $D$ is located on $BC$, and the circular arc $AD$ has centre $C$.