(i)[3]
the perimeter belonging to the metal plate.
(ii)[3]
the area belonging to the metal plate.
(iii)[2]
The shaded and unshaded pieces are now given to have equal area. Find $\alpha$ in terms of $\pi$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram illustrates a metal plate formed by fixing together two pieces, $OABCD$ (shaded) and $OAED$ (unshaded). The piece $OABCD$ is a minor sector of a circle with centre $O$ and radius $2r$. The piece $OAED$ is a major sector of a circle with centre $O$ and radius $r$. Angle $AOD$ is $\alpha$ radians. Simplify your answers where possible and find, in terms of $\alpha$, $\pi$ and $r$.