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

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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 forced by the corresponding chord [Use π=22/7]

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Radius (r) of circle = 21 cm

Angle subtended by the given arc = 60°

Length of an arc of a sector of angle θ =

=1/6 x 2 x 22 x 3

=22 cm

Area of sector OACB =

=1/6 x 22/7 x 21 x 21

=231 cm2

In ΔOAB,

∠OAB = ∠OBA (As OA = OB)

∠OAB + ∠AOB + ∠OBA = 180°

2∠OAB + 60° = 180°

∠OAB = 60°

Therefore, ΔOAB is an equilateral triangle.

Area of ΔOAB =

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