Concentric Circles do not Intersect

Theorem
If two circles are concentric, they share no points on their circumferences.

Alternatively, this can be worded:
 * If two concentric circles share one point on their circumferences, then they share them all (that is, they are the same circle).

Proof
This follows directly from:
 * Intersecting Circles Have Different Centers;
 * Touching Circles have Different Centers.