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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 π = 3.14 and √3 = 1.73)

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Answer:
HERe IS UR AnS:

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 × π × r^2

360

= 60 × 3.14 × ( 15)^2

360

= 117.75 cm^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 = 15 cos 30

= 15 √3

2

= 15 × 1.73

2

= 12.975 cm

∴ Area of △AOB=0.5×15×12.975

=97.3125cm^2

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

=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

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