If a chord of a circle of radius 28 cm

Question:

If a chord of a circle of  radius 28 cm makes an angle of 90 ° at the centre, then the area of the major segment is

(a) $392 \mathrm{~cm}^{2}$

(b) $1456 \mathrm{~cm}^{2}$

(c) $1848 \mathrm{~cm}^{2}$

(d) $2240 \mathrm{~cm}^{2}$

Solution:

Area of major segment,

$=$ Area of circle $-\left[\frac{\pi \theta}{360}-\sin \frac{\theta}{2} \cos \frac{\theta}{2}\right](r)^{2}$

$=\pi(28)^{2}-\left(\frac{\pi}{4}-\frac{1}{2}\right)(28)^{2}$

$=784 \pi-196(\pi-2)$

$=2240 \mathrm{~cm}^{2}$