Question

6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas
of the corresponding minor and major segments of the circle.
(Use Te = 3.14 and 13 = 1.73)​

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 °

at O.

Area of sector AOB=

=60/360 ×π×r ²

= 60/360 ×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

=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

=686.0625cm²

@ananya

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