Q. 205.0( 3 Votes )
Find the area of
Radius of circle, r = 42 cm
Let the angle of sector be θ with corresponding arc AB
We know that length of an arc
Where, θ is the angle of sector to the corresponding arc and 'r' is radius of circle.
As the length of arc is 44 cm. Putting values we get,
⇒ θ = 60°
Also, In ΔOAB
OA = OB [radii of same circle]
∠OBA = ∠OAB [Angles opposite to equal sides are equal]
∠OBA + ∠OAB + ∠AOB = 180° [Angle sum property]
⇒ ∠OBA + ∠OBA + θ = 180°
⇒ 2∠OBA + 60° = 180°
⇒ ∠OBA = 60°
⇒ ∠OBA = ∠OAB = ∠AOB = 60°
⇒ OAB is an equilateral triangle.
And area of equilateral triangle with side 'a'
Also, area of a sector
Where, θ is angle of sector and 'r' is the radius of circle.
Area of sector OAB
Area of required segment = area of sector OAB - area of ΔOAB
= (924 - 441√3) cm2
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