Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram represents sector $OAB$, with centre $O$ and radius $11\,\text{cm}$. The angle $AOB$ is $\alpha$ radians. Points $C$ and $D$ are on $OA$ and $OB$ respectively. Arc $CD$ is centred at $O$ and has radius $5\,\text{cm}$.
(i)[3]
The area of the shaded region $ABDC$ is $k$ times the area of the unshaded region $OCD$. Determine $k$.
(ii)[4]
The perimeter of the shaded region $ABDC$ is twice the perimeter of the unshaded region $OCD$. Determine the exact value of $\alpha$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct sector-area expressions” …