Mathematics 9709 · AS & A Level · Circular measure

Circular measure — practice question

The diagram depicts a motif made up of the major arc $AB$ of a circle with radius $r$ and centre $O$, together with the minor arc $AOB$ of another circle that also has radius $r$ but centre $C$. Point $C$ lies on the circle centred at $O$.
(a)[1]

Given that angle $ACB = k\pi$ radians, state the fraction $k$.

(b)[1]

State the perimeter, in terms of $\pi$ and $r$, of the shaded motif.

(c)[5]

Find the area of the shaded motif, with your answer expressed in terms of $\pi$, $r$ and $\sqrt{3}$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: The correct value is $k=\frac23$

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