Question 15
The diagram shows 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)** It is given that the area of the triangle $ABC$ is $4\ \text{cm}^2$ and the area of the sector $ABC$ is $8\alpha\ \text{cm}^2$.
Find the exact area of the shaded segment.
