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Question

Four equal circles, each of radius a, touch each other. Show that the area between them is 67a2 (Take π=227)

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Solution

The four circles can be arranged as:

Here, radius of each circle = a

∴ Each side of square = 2a

∴ Area of square = (2a)2 = 4a2

Area of all the four sectors area equal,

∴ Area of 4 sectors = 4 × area of each sector

= 4 x 90 360 x π x a2

= 4 x 14 x π x a2

= 14 x π x a2

Required area = Area of square – area of 4 sectors

=4 x a2 - 227 x a2

= a2 ( 4 - 227 )

= a2 x 67 )

= 67 ) a2

Hence, area between the circles is = 67 a2


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