No, not of their own impetus.
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No matter how you turn a circle, it will always be in the same position, therefore circles have infinite amounts of lines of symmetry.
Yes. The circles can be of different size. These are called concentric circles.
concentric circles
A cylinder has two circles as its bases.
Tangent circles are circles that touch one another without crossing. The distance between the centres of the circles must be equal to the difference or the sum of their radii.