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.

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