(i)[3]
Show that the angle $POQ$ is $\frac{\pi}{4}$ radians.
(ii)[2]
Find the perimeter of the shaded region.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram illustrates a circle $C$ with centre $O$ and radius $3\,\text{cm}$. The radii $OP$ and $OQ$ are produced to $S$ and $R$ respectively, making $ORS$ a sector of a circle centred at $O$. Given that $PS = 6\,\text{cm}$ and that the shaded region has the same area as circle $C$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate use of the sector area formula to form an equation in $\theta$” …
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