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


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