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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 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 B a2(4π4)
Area of Interior region = Area of square Total area of circles inside the square
Area of square = side2 = a2
Area of portion of 4 circles = 4×(14πr2) =4×(14π(a2)2) = πa24
Thus, area of Interior region = a2πa24
= a2(4π4)
238501_206596_ans.png

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