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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 =
Length of arc ACB =
= 22 cm
Area of sector OACB =
In ΔOAB,
∠OAB = ∠OBA (As OA = OB)
Question 4:
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:
(i) Minor segment
(ii) Major sector
[Use π = 3.14]
Let AB be the chord of the circle subtending 90° angle at centre O of the circle.
Area of major sector OADB =
Area of minor sector OACB =
Area of ΔOAB =
= 50 cm2
Area of minor segment ACB = Area of minor sector OACB −
Area of ΔOAB = 78.5 − 50 = 28.5 cm2
Question 5:
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
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°
Therefore, ΔOAB is an equilateral triangle.
Area of ΔOAB =
Area of segment ACB = Area of sector OACB − Area of ΔOAB
