Question

chord of a circle of radius 21 cm subtends angle 60° at the centre. find the area of corresponding minor segment of the circle​

Answer 1

Step-by-step explanation:

Radius (r) of circle = 21 cm

Angle subtended by the given arc = 60°

Length of an arc of a sector of angle θ =

Length of arc ACB =

= 22 cm

Area of sector OACB =

In ΔOAB,

∠OAB = ∠OBA (As OA = OB)

∠OAB + ∠AOB + ∠OBA = 180°

2∠OAB + 60° = 180°

∠OAB = 60°

∴ ΔOAB is an equilateral triangle.

Area of ΔOAB =

Area of segment ACB = Area of sector OACB − Area of ΔOAB