Drawing the image of a circle under reflection through its center?

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Would the image of a circle of radius r, center P under a reflection through its center remain in the same position? I am guessing that it is, but unfortunately I've found no other sources that verify this answer.

Thanks!

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The geometry stays the same,that is we still see the same graph.

The points on the circle move around such that their images under the reflection form the same circle.