Assertion: Two Circles Are Equal If Their Radii Are Equal
When two circles are described as equal, it implies that they are identical in all their geometric properties. One of the fundamental properties of circles is their radius.

Key Points:
- Definition of Equal Circles:
- Two circles are considered equal if they have the same radius. This means that every point on the circumference of one circle is equidistant from its center, just like the other circle.
- Radius as a Defining Feature:
- The radius of a circle is the distance from the center to any point on the circumference. If two circles have equal radii, they will have the same distance from their respective centers to their circumferences.
- Circumference and Circle Properties:
- The circumference of a circle is calculated using the formula \(C = 2\pi r\), where \(r\) is the radius. If the radii are equal, the circumferences will also be equal, reinforcing the circles' equality.
- Centers of the Circles:
- While two equal circles may have different centers, the equality of their radii ensures that the shape and size of the circles remain consistent.
- Conclusion:
- Therefore, the assertion holds true: If two circles are equal, then their radii must indeed be equal. This relationship is crucial in the study of geometry, particularly in understanding properties of circles and their applications.
In summary, the equality of circles is fundamentally tied to the equality of their radii, which determines their circumference and overall geometric similarity.