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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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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 2πr^{2})

= θ/360 x πr^{2}

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 cm^{2}

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