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

विकल्प

• 120.56 cm²

• 124.63 cm²

• 118.24 cm²

• 130.57 cm²

Answer 1

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).