There are infinite diameters in a circle all of the same lengths.
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A diameter is the size of a circle from edge to edge when measuring through the centre. Consequently, as a circle can be any size, there can be any number of centimetres in the diameter..
Infinitely many. Each point on the circumference of a semicircle can be one end of a diameter and there are infinitely many points in a line segment of any length.
A circle has symmetry about any line drawn through its center. Your answer is, "yes".
The center of a circle is the same for all circles but the length of the radius can change
radius