Question

The radius of a circle with centre O is 6 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the minor and major segments.

Answer 1

The triangle OAB is a right isosceles triangle.

Area of triangle OAB = $\frac{1}{2}\times 6\times 6=18{\mathrm{cm}}^2$

Now,
Area of the minor segment:
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{sector}-\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle} \\ \Rightarrow \left(\frac{90}{360}\times \mathrm{\pi }\times 36\right)-18 \\ =10.26{\mathrm{cm}}^2 \end{gathered}$$

Area of the major segment:
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{circle}-\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{minor}\mathrm{segment} \\ \Rightarrow \left(\mathrm{\pi }\times 36\right)-\left(9\mathrm{\pi }-18\right) \\ =27\mathrm{\pi }+18 \\ =102.78{\mathrm{cm}}^2 \end{gathered}$$