Question

The radius of a circle with centre O is 5 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB (Take $\pi =3.14$)

Answer 1

Area of minor segment $=\pi r^2\times \frac{\theta }{{360}^o}-r^{2}sin\frac{\theta }{2}cos\frac{\theta }{2}$

$=3.14\times 5\times 5\times \frac{90}{360}-5\times 5\times \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}$

$=19.625-12.5=7.125c{m}^2$

Now, area of the major segment = Area of circle - Area of minor segment

$=3.14\times 5\times 5-7.125$

$=78.5-7.125=71.375c{m}^2$