Q5 of 52 Page 159

A chord PQ of a circle with radius 15 cm subtends an angle of 60° with the centre of the circle. Find the area of the minor as well as the major segment. (π = 3.14)


Radius of circle, r = 15cm


Central angle, θ = 60°


Since the angle subtended at centre is 60°


And by the property, if two sides of a triangle are equal then their corresponding angles are also equal.


⇒ ∠ OQP = ∠ OPQ


As the sum of all internal angles of a triangle is equal to 180°


⇒ ∠ OQP = ∠ OPQ = 60°


⇒ Δ OPQ is an equilateral triangle.




AT = 97.32 sq.cm




⇒ AR = 117.75 – 97.32


⇒ AR = 20.43 sq.cm


Now,




⇒ AS = 706.5 – 20.43


⇒ AS = 686.07 sq.cm


∴ The area of minor segment and major segment is 20.43 sq.cm and 686.07 sq.cm respectively


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