A square does have a centre.
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A square can't have a circumference. That's only for circles squares have area, volume, or perimeter.
Of course not! There are an infinite number of smaller circles.
The question is misguided. You do not use radius only on circles!
Imagine 4 circles just touching, like this OO .............................................................. OO only closer. Draw a square connecting the centres of the 4 circles. Given the circles each have a radius of 10 metres the length of each side of the square is (10+10) =20 metres and the area of the square is 400 square metres. The area of each quarter of the circle that is within the square is one quarter of pi times r squared so the four quarters = 100pi square metres so the space between the circles is the difference.
Yes, circles that share one and only one point are tangent to each other.