When they have the same centre. As a consequence, the distance between the two circles, along any common radial ray, is a constant.
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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.
concentric
The use of concentric circles is most commonly used on a target. Concentric circles are placed around a target in which each concentric circle has the same center.
concentric
Concentric and coincident, perhaps.