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Four Equal Circles Each of Radius A, Touch Each Other. Show that Area Between Them is `6/7a^2` - CBSE Class 10 - Mathematics

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Question

Four equal circles each of radius a, touch each other. Show that area between them is `6/7a^2`

Solution

Let circles be with centres A, B, C, D]

Join A, B, C and D then ABCD is square formed with side = (a + a) = 2a

Radius = a

Area between circles = area of square – 4(area of quadrant)

(shaded region)

= (2๐‘Ž)2 − 4 (`1/4`๐‘Ž๐‘Ÿ๐‘’๐‘Ž ๐‘œ๐‘“ ๐‘๐‘–๐‘Ÿ๐‘๐‘™๐‘’ ๐‘ค๐‘–๐‘กโ„Ž ๐‘Ÿ๐‘Ž๐‘‘๐‘–๐‘ข๐‘  ′๐‘Ž′)

=` 4a^2 − 4 (1/4) × a^2`

= ๐‘Ž2(4 − ๐œ‹)

= ๐‘Ž2 (4 −`22/7`)
= `((28−22)/7) a^2 =6/7a^2`
∴ Area between circles =`6/7a^2.`

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Solution Four Equal Circles Each of Radius A, Touch Each Other. Show that Area Between Them is `6/7a^2` Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle.
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