What is the relationship between the diameter and the radius?

The relationship between the diameter and the radius of a circle is fundamentally defined in geometry. The diameter of a circle is the longest straight line that can be drawn through the center, reaching from one point on the circumference to another point directly opposite. The radius, on the other hand, is the distance from the center of the circle to any point on its circumference.

Mathematically, the diameter is defined as being twice as long as the radius. This can be expressed with the formula: diameter = 2 × radius. Therefore, if you know the radius, you can easily find the diameter by multiplying by two. This direct relationship holds true for all circles and is one of the basic properties of circular geometry.

The other options do not accurately describe the relationship between these two measurements. The statement that the radius is twice the diameter is incorrect because it reverses the relationship. Similarly, stating that the diameter equals the radius or that the diameter is half the radius is also incorrect, as it misunderstands the fundamental definitions of these two terms. This clear distinction is key for understanding how circles function in geometry.