I would think there would be an infinite number of lines of symmetry. Any line passing through the center of the circle, regardless of the angle will be a symmetry line.
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A circle has lines of symmetry that are infinite
There are 180 lines of symmetry in a circle.
There are infinite lines of symmetry within a circle
There are infinitely many lines of symmetry on a circle.
A circle has infinite lines of symmetry caused by its diameter which can be rotated inside the circle.