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Byju's Answer
Standard X
Mathematics
Area of a Segment of a Circle
A chord PQ ...
Question
A chord
P
Q
of a circle of radius
10
c
m
subtends an angle of
60
∘
at the centre of the circle Find the area of major and minor segments of the circle.
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Solution
Minor segment
=
P
S
Q
O
Major segment
=
P
T
Q
O
Area of PSQO = angle in radian subtend by the segment
×
(
r
a
d
i
u
s
)
2
=
θ
∘
π
360
×
r
2
=
60
360
π
×
(
10
)
2
=
π
6
×
100
=
50
π
3
sq. cm
Similarly
∠
subtend by PTQO at center
=
360
−
60
=
300
∘
Area of PTQO
=
300
360
π
×
(
10
)
2
=
5
π
6
×
100
=
250
π
3
sq. cm
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Q.
A chord PQ of a circle of radius 10 cm subtends an angle of 60° at the centre of the circle. Find the area of major and minor segments of the circle.