Question

a chord of a circle of radius 5cm subatends an angle of 45°at the centre . find the area of minor segmants of circle​

Answer 1

Answer:

In the mentioned figure,

O is the centre of circle,

AB is a chord

AXB is a major arc,

OA=OB= radius = 15 cm

Arc AXB subtends an angle 60

o

at O.

Area of sector AOB=

360

60

×π×r

2

=

360

60

×3.14×(15)

2

=117.75cm

2

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

By trigonometry,

AC=15sin30

OC=15cos30

And, AB=2AC

∴ AB=2×15sin30=15 cm

∴ OC=15cos30=15

2

3

=15×

2

1.73

=12.975 cm

∴ Area of △AOB=0.5×15×12.975=97.3125cm

2

∴ Area of minor segment (Area of Shaded region) =117.75−97.3125=20.4375 cm

2

Area of major segment = Area of circle − Area of minor segment

=(3.14×15×15)−20.4375

=686.0625cm

2