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)


Radius of the circle = r = 12 cm


OA = OB = 12 cm


AOB = 60° (given)


Since triangle OAB is an isosceles triangle, OAB = OBA = θ (say)


Also, Sum of interior angles of a triangle is 180°,


θ + θ + 60° = 180°


2θ = 120° θ = 60°


Thus, the triangle AOB is an equilateral triangle.


AB = OA = OB = 12 cm


Area of the triangle AOB = × a2 ,


where a is the side of the triangle.


× (12)2


= (√3/16) ×144


=


= 62.354 cm2


Now, Central angle of the sector AOBCA = = 60° = = (π/3) radians


Thus, area of the sector AOBCA =



= = 75.36 cm2


Now, Area of the segment ABCA = Area of the sector AOBCA – Area of the triangle AOB


= (75.36 – 62.354) cm2 = 13.006 cm2


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