Question

A chord of a circle of radius 18 cm subtends an angle of 120° at the centre. Find the
area of the corresponding (1) minor sector and (ii) major segment (use 1-3.14 and
13=1.73).​

Answer 1

Draw OM AB in figure

(RHS congruence)

AOM=BOM

BOM = (cpct)

In OMA

cos 60o =



OM = 6 cm

and sin 60o =

AM = 6 cm

ar AOB = AB OM = AM OM = 36 cm2

area of segment AXB

= area of sector OAXB - ar AOB

= 3.14 12 12 - 36

= (150.72 - 36) cm2

= 88.36 cm2