The inscribed square problem!
Four circles of equal size are inscribed in a square.
Inside of the four circles is a smaller square, tangent to each of the 4 circles.
If the large has a side length equal to 4, what is the area of the smaller square? Give your answer to 3 decimal place.
The answer is 0.686.
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1 solution
Side length of small square equals half the diagonal of the large square minus the diameter of 1 circle. Diameter of a circle is 2 and the half diagonal is found by Pythagoras and equal 2 2 . So the area of the small square is: ( 2 2 − 2 ) 2 ≈ 0 . 6 8 6 .