Question

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

Answer 1

Radius of the circle $=14cm$

Central angle for minor sector $={90}^{\circ }$

Area of the minor sector $=\frac{\theta }{360}\times \pi r^2$

$=\frac{{90}^{\circ }}{360}\times \frac{22}{7}\times {14}^2$

$=22\times 7=154c{m}^2$

So, area of minor segment = Area of sector - Area of triangle AOB

$=154-\frac{1}{2}\times 14\times 14=154-98=56c{m}^2$

Area of the major sector= Area of circle - Area of minor segennt

$=\pi \times {14}^2-56$

$=\frac{22}{7}\times 14\times 14-56$

$=616-56=560c{m}^2$