(a)[3]
Find $CD$ expressed in terms of $r$ and $\sin \theta$.
(b)[3]
Now take $r = 4$ and $\theta = \frac{\pi}{6}$. Find the perimeter of sector $CAB$ in terms of $\pi$.
(c)[4]
Find the shaded region’s area in terms of $\pi$ and $\sqrt{3}$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram displays a sector $CAB$ from a circle centred at $C$. Inside the sector is a circle with centre $O$ and radius $r$; it touches the sector at $D$, $E$ and $F$, with $COD$ forming a straight line and angle $ACD$ equal to $\theta$ radians.