(i)[2]
Show that angle $AOB = \frac{1}{3}\pi$ radians.
(ii)[3]
Express, in terms of $r$, $\pi$ and $\sqrt{3}$, the perimeter of the shaded part.
(iii)[2]
Express, in terms of $r$, $\pi$ and $\sqrt{3}$, the area of the shaded part.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
In the figure, $AB$ is a circular arc with centre $O$ and radius $r$. The segment $XB$ touches the circle at $B$, and $A$ is the midpoint of $OX$.