1. **State the problem:** We have two circles with the same center $P$, and we need to determine which statement about their relationship and points of intersection is true. 2. **Key definitions:** - *Concentric circles* are circles that share the same center but have different radii. - *Congruent circles* have the same radius. - *Similar circles* always hold true since all circles are similar by definition. - The number of intersection points depends on the relative positions and radii of the circles. 3. **Analyze the given information:** - The circles share the same center $P$, so they are concentric. - The circles do not intersect at any point. - Since they have the same center but do not intersect, their radii must be different. 4. **Evaluate each option:** - "The circles are congruent and have 0 points of intersection." This is false because congruent circles with the same center would coincide, having infinite points of intersection. - "The circles are concentric and have 0 points of intersection." This is true because concentric circles with different radii do not intersect. - "The circles are congruent and have 1 point of intersection." False, congruent circles with the same center coincide. - "The circles are similar and have 1 point of intersection." False, similar circles always have the same shape but here they do not intersect. **Final answer:** The correct statement is: **The circles are concentric and have 0 points of intersection.**