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 $k=\frac23$” …