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So I have a circle with an infinite circumference and the natural numbers are spaced 1 unit away from each other at the edge of the circle. Now I draw a line from each natural number

to the center of the circle. Now is there a point from the center of the circle at a finite distance such that there are no gaps in a second test circle drawn at this finite distance.

And then can I construct a circle with infinite circumference and have an uncountable number of points and each point is separated from the other by a positive finite distance.

And then draw a line from each point to the center of my circle. will I have another circle inside this that has no gaps in it.