A chord AB of a circle, of radius 14 cm makes an angle of 60° at the centre of the circle. Find the area of the minor segment of the circle.(Use π=22/7)
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Area of the minor segment = 17.8 cm²
Step-by-step explanation:
Given radius = 14 cm.
Angle of the sector = 60 degrees.
Area of the sector = (θ/360)(πr²)
= 60/360 * 22/7 * 14 * 14
= 22 * 14 * 2/ 12
= 102.67 cm²
The perpendicular will suspend an angle of 30 degrees at the center. So height of the triangle:
Cos 30 = adjacent/hypotenuse
√3 / 2 = height/14
height = 7√3
Sin 30 = opposite/hypotenuse
1/2 = base/2 / 14
base = 14
Area of the triangle = 1/2 * height * base.
= 1/2 * 14 * 7 √3
= 84.87 cm²
Area of the minor segment = 102.67 - 84.87 = 17.8 cm²
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