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

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

• A. Radius is half of the diameter.
• B. Radius equals the diameter.
• C. Radius is twice the diameter.
• D. Radius plus diameter equals circumference.

Answer: (A)

The key idea is that the diameter spans the circle through the center and is made up of two radii. So its length is twice the radius, meaning the radius is half the diameter. For example, if the radius is 5 units, the diameter is 10 units. The other options would imply relationships that don’t hold true—radius equaling diameter would make them the same length, radius being longer than the diameter isn’t possible since the diameter already covers the full breadth across the circle, and radius plus diameter isn’t related to the circumference in that way.

The key idea is that the diameter spans the circle through the center and is made up of two radii. So its length is twice the radius, meaning the radius is half the diameter. For example, if the radius is 5 units, the diameter is 10 units. The other options would imply relationships that don’t hold true—radius equaling diameter would make them the same length, radius being longer than the diameter isn’t possible since the diameter already covers the full breadth across the circle, and radius plus diameter isn’t related to the circumference in that way.