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Concentric circles are the circles with the same center therefore they do not cross with each other as the "center is not considered a point on the circle". An exception would be two circles that are concentric and have the same radius, in which case the circles are indistinct and every point of the circles is an intersection.

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Q: Is the center of a circle the point of intersection for two concentric circles?
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Are coplanar circles that have the same center called concentric circles?

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