(a)[2]
Show that $BC$ has exact length $r\sqrt{5 - 2\sqrt{3}}$.
(b)[2]
Find the exact perimeter of the shaded figure.
(c)[3]
Find the exact area of the shaded figure.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram shows $OAB$ as a sector of a circle with centre $O$ and radius $2r$, with angle $AOB = \frac{\pi}{6}$ radians. Point $C$ lies halfway along $OA$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use cosine rule $BC^2=r^2+4r^2-2r\cdot2r\cos(\frac{\pi}{6})$” …
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