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A chord AB of a circle of radius 14cm makes a right angle at the centre of the circle. Find the area of the minor segment.
CBSE class-10 math areas-related-to-circles
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A chord AB of a circle of radius 14cm makes a right angle at the centre of the circle. Find the area of the minor segment.

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peter
Asked by peterrep:837
University of Lagos Nigeria
01 August 2020

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judziy
Judziy answeredrep:799
University of Benin Nigeria
01 August 2020
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Area of the segment (shaded portion) = Area of sector ACB - Area of triangle ACB

∠ACB = 90 [because it's a right angle].

Area of sector ACB = 1/2 (length of arc x radius)

length of arc = θ/360 x 2πr

Area of sector ACB = 1/2 (θ/360 x 2πr x r)

= 1/2 (θ/360 x 2πr2)

= θ/360 x πr2

where r is the radius.

r = 14cm

θ= 90

Thus, area of sector ACB = 90/360 x π x (14)2

= 49π

but, π = 22/7

Area of sector ACB = 49 x 22/7

= 154

Area of triangle ACB = 1/2 base x height

= 1/2 x 14 x 14

= 98

Therefore, area of the segment = 154 - 98

= 56 cm2

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