What is the relationship between the diameter and the radius of a circle?

The diameter of a circle is defined as the longest distance across the circle, passing through the center and touching two points on its boundary. The radius, on the other hand, is the distance from the center of the circle to any point on its boundary.

The relationship between the diameter and the radius is that the diameter is double the length of the radius. This can be expressed mathematically as:

Diameter = 2 × Radius

This means that for any given radius, if you multiply it by 2, you will get the diameter. For example, if the radius of a circle is 3 units, the diameter would be 2 × 3 = 6 units. This fundamental relationship holds true for all circles, making choice A the correct answer.

In contrast, the other options do not accurately describe the relationship. The radius being twice the length of the diameter or being equal to the diameter are incorrect interpretations of how these two measurements relate to each other. Similarly, stating that the radius is half of the diameter is a misunderstanding; although this is true, it does not capture the direct relationship given in the correct answer. Understanding this relationship is crucial for solving various problems involving circles in geometry.