Question

A chord of a circle radius $14$ cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle.

Answer 1

Given $radius\left(r\right)=14cm$

$\Rightarrow$ Area of sector $OABO=\frac{\theta }{{360}^o}\pi r^2$

$\therefore$ Area of sector $OABO=\frac{{90}^o}{{360}^o}\times \frac{22}{7}\times (14{)}^2=154c{m}^2$

$\Rightarrow$ Area of right angled $△OAB=\frac{1}{2}\times 14\times 14=98c{m}^2$

$\therefore$ Area of the minor segment of the circle $=$ Area of sector $OABO$ - Area of righta angled $△ABO$

$\therefore$ Area of the minor segment of the circle $=(154-98)c{m}^2=56c{m}^2$

$\Rightarrow$ Area of circle $=\pi r^2=\frac{22}{7}\times 14\times 14=616c{m}^2$

$\Rightarrow$ Area of the major segment of the circle = Area of circle - Area of minor segment.

$\therefore$ Area of the major segment of the circle $=(616-56)c{m}^2=560c{m}^2$