Question

The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major
segments.

Answer 1

Area of minor segment = Area of sector AOBC − Area of right triangle AOB
$$\begin{gathered} =\frac{90°}{360°}\mathrm{\pi }{\left(\mathrm{OA}\right)}^2-\frac{1}{2}\times \mathrm{OA}\times \mathrm{OB} \\ =\frac{1}{4}\times \frac{22}{7}\times {\left(7\right)}^2-\frac{1}{2}\times 7\times 7 \\ =\frac{1}{4}\times \frac{22}{7}\times {\left(7\right)}^2-\frac{1}{2}\times 7\times 7 \\ =38.5-24.5 \\ =14{\mathrm{cm}}^2 \end{gathered}$$
Area of major segment APB = Area of circle − Area of minor segment
$$\begin{gathered} =\mathrm{\pi }{\left(\mathrm{OA}\right)}^2-14 \\ =\frac{22}{7}\times {\left(7\right)}^2-14 \\ =154-14 \\ =140{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of major segment is 140 cm² .