Question

A chord $PQ$ of a circle of radius $10cm$ subtends an angle of ${60}^{\circ }$ at the centre of the circle Find the area of major and minor segments of the circle.

Answer 1

Minor segment $=PSQO$

Major segment $=PTQO$

Area of PSQO = angle in radian subtend by the segment $\times (radius{)}^2$

$=\frac{{\theta }^{\circ }\pi }{360}\times r^2$

$=\frac{60}{360}\pi \times (10{)}^2$

$=\frac{\pi }{6}\times 100=\frac{50\pi }{3}$ sq. cm

Similarly $\angle$ subtend by PTQO at center

$=360-60={300}^{\circ }$

Area of PTQO $=\frac{300}{360}\pi \times (10{)}^2$

$=\frac{5\pi }{6}\times 100=\frac{250\pi }{3}$ sq. cm