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Question
In a circle of radius 14 cm, an arc subtends an angle of 120° at the centre. If `sqrt(3) = 1.73` then the area of the segment of the circle is
Options
120.56 cm2
124.63 cm2
118.24 cm2
130.57 cm2
Solution
Radius of the circle, r = 14 cm
Draw a perpendicular OD to chord AB. It will bisect AB.
∠A = 180 - (90° + 60°) = 30°
`"cos" 30^circ = "AD"/"OA"`
`=>sqrt(3)/2 = "AD"/14`
`=>"AD" = 7sqrt(3)`
`=> "AB" = 2xx"AD"=14sqrt(3) "cm"`
`"sin" 30^circ = "OD"/14`
`=> 1/2 = "OD"/14`
⇒ OD = 7 cm
Area of minor segment = Area of sector OAPB − Area of triangle AOB
`=theta/360^circpi("OA")^2-1/2xx"OD"xx"AB"`
`=120^circ/360^circxx22/7(14)^2- 1/2xx7xx14sqrt(3)`
=205.33 - 84.77
= 120.56 cm2
Hence, the correct answer is option (a).
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