(a)[3]
With $\theta = \dfrac{1}{6}\pi$ given, determine the exact area of $BCD$ in terms of $r$.
(b)[4]
If instead the length of $BD$ is $\dfrac{\sqrt{3}}{2}r$, determine the exact perimeter of $BCD$ in terms of $r$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts sector $ABC$ from a circle whose centre is $A$ and whose radius is $r$. The line $BD$ is at right angles to $AC$. The angle $CAB$ is $\theta$ radians.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the sector area formula $\frac{1}{2}r^2\theta$ with $\theta=\frac{\pi}{6}$.” …
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