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

The relationship between the diameter and radius of a circle is that the diameter is twice the length of the radius. This can be understood by considering the definitions of both terms:

• The radius (r) is defined as the distance from the center of the circle to any point on its circumference.
• The diameter (d) is the distance across the circle, passing through the center, effectively connecting two points on the circumference.

Since the diameter consists of two radii (one extending from the center to one side of the circle, and the other from the center to the opposite side), it follows that the diameter can be expressed as d = 2r. This foundational relationship is critical in various mathematical applications involving circles, such as calculating circumference and area, where these relationships frequently come into play.