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A square does have a centre.
Concentric circles - are circles that share a common centre. A typical example - is dripping water into a bowl - where you'll see the ripples form and spread out to the edge of the container.
No not all circles have the same centre. If the circles formula is in the form x2+ y2=r2 then the centre is always the origin= (0,0). But if the formula for the circle is in the form (x-h)2+(y-k)2= r2 then the centre is the the opposite sign of the h and the k. Eg. (x+4)2+(y-9)2=16 the centre would be (-4,9) and the radius would be 4
When they have the same centre. As a consequence, the distance between the two circles, along any common radial ray, is a constant.