1. **State the problem:** We want to find the distance from the center of a circle to its border. 2. **Formula and explanation:** The distance from the center of a circle to any point on its border is the radius $r$ of the circle. 3. **Important rule:** By definition, a circle is the set of all points that are exactly $r$ units away from the center. 4. **Intermediate work:** If you know the radius $r$, then the distance from the center to the border is simply $r$. 5. **Conclusion:** The distance from the center of a circle to its border is the radius $r$.