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
]
Radius (r) of circle = 15 cm
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
