Q. 54.2( 309 Votes )

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.

Answer :


Radius (r) of circle = 21 cm

The angle subtended by the given arc = 60°


Length of an arc of a sector of angle θ =


(i) Length of arc ACB = 

=  × 2 × 22 × 3


= 22 cm


(ii) Area of sector OACB =


=


= × × 21 × 21


= 231 cm2


(iii) In ΔOAB,

As OA = OB

⇒ ∠OAB = ∠OBA (Angles opposite to equal sides are equal)


⇒ ∠OAB + ∠AOB + ∠OBA = 180°


⇒  2∠OAB + 60° = 180°

⇒  2∠OAB  = 180° - 60° 

⇒  ∠OAB = 60°

Hence,

ΔOAB is an equilateral triangle


Area of equilateral triangle = (Side)2

⇒ 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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