Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
In the diagram, $AB$ forms an arc of a circle with centre $O$ and radius $6$ cm, and $AOB = \frac{\pi}{3}$ radians. The line $AX$ touches the circle at $A$, and $OBX$ lies on a straight line.
(i)[1]
Show that $AX$ has exact length $6\sqrt{3}$ cm.
(ii)[3]
Find the area of the shaded region, expressing your answer in terms of $\pi$ and $\sqrt{3}$.
(iii)[4]
Find the perimeter of the shaded region, giving your answer in terms of $\pi$ and $\sqrt{3}$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find $AX=6\tan\frac{\pi}{3}=6\sqrt{3}$ correctly” …