Question

A chord of a circle of radius $10cm$ subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (ii) major sector. (Use $\pi =3.14$)

Answer 1

In the mentioned circle,

O is the centre and AO $=$BO $=$ Radius $=$ 10 cm

AB is a chord which subtents 90${}^o$ at centre O, i.e., $\angle AOB={90}^o$

(i)

Area of minor segment APB (Shaded region) $=$ Area of Sector AOB - Area of $△$AOB

$=\left(\frac{\pi \times 10\times 10}{4}\right)-(0.5\times 10\times 10)$

$=78.5-50$

$=28.5c{m}^2$

(ii)

Area of Major sector $=$ Area of circle - Area of Sector AOB

$=$ $(\pi \times 10\times 10)-\left(\frac{\pi \times 10\times 10}{4}\right)$

$=314-78.5$

$=235.5c{m}^2$