Class 10 NCERT Maths Solution Exercise-12.2, Areas Related to Circles

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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 π = 3.14 and √3 = 1.73

Area of sector OPRQ =




In ΔOPQ,
∠OPQ = ∠OQP (As OP = OQ)
∠OPQ + ∠OQP + ∠POQ = 180°
2 ∠OPQ = 120°
∠OPQ = 60°
ΔOPQ is an equilateral triangle.
Area of ΔOPQ =



Area of segment PRQ = Area of sector OPRQ − Area of ΔOPQ
= 117.75 − 97.3125
= 20.4375 cm²
Area of major segment PSQ = Area of circle − Area of segment PRQ

Question 7:

A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.

[Use π = 3.14 and √3 = 1.73]

Let us draw a perpendicular OV on chord ST. It will bisect the chord ST.
SV = VT
In ΔOVS,






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