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Question
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the segment formed by the corresponding chord. (Use π = `22/7`)
Solution
Area of the segment APB = [Area of the sector AOB] − [Area of ΔAOB] ....(1)
In AOB, OA = OB = 21 cm
∴ ∠A = ∠B = 60° ...(∴ ∠O = 60°)
AOB is an equilateral triangle.
∴ AB = 21 cm
∴ Area of ΔAOB = `sqrt3/4` (side)2 ....[∴ ΔAOB is an equilateral triangle]
`= sqrt3/4 xx 21 xx 21 "cm"^2`
= `(441sqrt3)/4` cm2 ...(2)
Using part (ii) and (2) in (1), we have
Area of the segment = `[231 "cm"^2] − [(441sqrt3)/4 "cm"^2]`
`= (231 - (441sqrt3)/4) "cm"^2`
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