- 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.
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 =
∠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
Length of the Arc = (2πrθ/360°)
Here r = 21 cm and θ = 60°
Length of the Arc = (2π*21*60°/360°) Aftr putting π = 22/7
Length of the Arc = 22cm
Area of a sector = (πr2θ/360°)
= (π21260/360°) Aftr putting π = 22/7
Area of a sector = 231 cm square.
Third potion would tk a diagram. Not possible at my end.