Question

A chord of a circle of radius 12 cm. subtends an angle of 120° at the centre. Find the area
of the corresponding minor segment of the circle (use r=3.14 and V3 = 1.732​

Answer 1

Answer:

Answer

In the mentioned figure,

O is the centre of circle,

AB is a chord

AYB is a major arc,

OA=OB= radius =12 cm

Arc AYB subtends an angle 120

o

at O.

i) Area of Sector AOB=

360

120

×π×r

2

=150.72cm

2

ii) Area of the segment (Area of Shaded region) = Area of sector AOB− Area of △AOB

By trigonometry,

AC=12sin60

o

OC=12cos60

o

And, AB=2AC

∴ AB=2×12×

2

3

=20.76 cm

∴ OC=6 cm

∴ Area of △AOB=0.5×20.76×6=62.28cm

2

∴ Area of segment (Area of Shaded region) =150.72−62.28=88.44 cm

2