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Question
Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60° (Use π = 3.14).
Solution
Radius of the circle = r = 12 cm
OA = OB = 12 cm
∠AOB = 60° .......(GIven)
As triangle OAB is an isosceles triangle,
∠OAB = ∠OBA = θ .....(Let)
And sum of interior angles of a triangle is 180°,
θ + θ + 60° = 180°
2θ = 120°
θ = 60°
Therefore, the triangle AOB is an equilateral triangle.
AB = OA = OB = 12 cm
Area of the triangle AOB = `(sqrt(3)/4) xx a^2`.
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