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).

Answer 1

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`.