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

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

(i) the length of the arc

(ii) area of the sector formed by the arc

(iii) area of the line segment formed by the corresponding chord.

answered Nov 9, 2017 by Expert (2,179 points)

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

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