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Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded area enclosed between the circles is

24/7cm2. Find the radius of each circle.


Shaded area = area of square - sum of areas of 4 quadrants
Let the radius of circle be r cm
then side of square will be 2r cm
24/7 = (2r)² - 4×(1/4)×πr²
        =4r² - 22/7 r²
⇒24/7 = 6r²/7
⇒r² =4
⇒r =2 cm
hence , the radius of each circle is 2 cm
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