Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts a sector $ABC$ of a circle with centre $A$ and radius $r$ cm. The angle $BAC$ is $\alpha$ radians, where $0 < \alpha < \frac{1}{2}\pi$.
(a)[4]
The area of triangle $ABC$ is $4\text{ cm}^2$, and the area of sector $ABC$ is $8\alpha\text{ cm}^2$. Find the exact area of the shaded segment.
(b)[4]
Here, the chord $BC$ has length $\frac{1}{\sqrt{2}}r$ cm, but the area of triangle $ABC$ remains $4\text{ cm}^2$. Determine the area of the shaded segment. Give your answer correct to $3$ significant figures.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the sector/triangle relationship to find $r=4$.” …