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Question

ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let δ be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of δ is

A
a2(1π)
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B
a2(4π4)
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C
a2(π1)
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D
πa24
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Solution

The correct option is D a2(4π4)
Area of shaded region, δ=a2πa24
=a2[1π4]=a2[4π4]

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