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A rotation turns a shape through an angle about a fixed point
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infinite.. you can have different sizes of circles crossing at the same point.. so it can literally be an infinite amount
Infinite lines because a circle has infinite lines of symmetry.
The center of the circle. That's how the circle is defined. (The collection of all points on a plane equidistant from a fixed point. The fixed point is the center and the fixed distance is the radius.)