(i)[3]
Find the value of $\alpha$ in terms of $\pi$.
(ii)[2]
Find the perimeter of the complete figure in terms of $\pi$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram shows that $OAB$ is a sector of a circle with centre $O$ and radius $8\text{ cm}$. The angle $BOA$ equals $\alpha$ radians. $OAC$ is a semicircle whose diameter is $OA$. The area of the semicircle $OAC$ is twice the area of the sector $OAB$.