In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:

(i) The length of the arc

(ii) Area of the sector formed by the arc

(iii) Area of the segment formed by the corresponding chord.

Radius (r) of circle = 21 cm

Angle subtended by the given arc = 60°

Length of an arc of a sector of angle θ = * 2r

(i) Length of arc ACB = * 21

= * 2 * 22 * 3

= 22 cm

(ii) Area of sector OACB = * r²

= * * 21 * 21

= 231 cm²

(iii) In ΔOAB,

∠OAB = ∠OBA (As OA = OB)

∠OAB + ∠AOB + ∠OBA = 180°

2∠OAB + 60° = 180°

∠OAB = 60°

Hence,

ΔOAB is an equilateral triangle

Area of ΔOAB = (Side)²

= * (21)²

= cm²

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

= (231 - ) cm²