Circles have properties that are common to all of them. One such property is the relationship between a circle's diameter and its radius. You can use this property, when it's expressed as an equation, to solve for the radius of any circle, as long as you know that circle's diameter.
The Definition of Diameter
Imagine that you can draw a dot in the direct center of a circle. If you draw a line from one edge of the circle through the dot to the opposite edge of the circle, you have drawn the diameter. Another way to look at the diameter is to think of it as a line that divides the circle into two equal halves.
The Definition of Radius
Imagine that same circle with a dot in its center. If you draw a line from the dot to the edge of the circle, you have drawn a radius. Note that the radius does not divide the circle into two parts since it does not go across the whole circle. Also, you can draw the line from the center dot to the edge in any direction to make a radius. All the radii, plural for radius, of a circle have the same length.
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The Relationship Between Diameter and Radius
Once you know the definitions of diameter and radius, the relationship between them is simple to imagine.The diameter of a circle is twice as long as any radius of the same circle. The equation below shows this relationship. In the equation, d stands for diameter and r stands for radius.
d = 2r
Finding the Radius from the Diameter
To find the radius of a circle whose diameter you know, you must first rearrange the equation for diameter to solve for the radius. You can do that by dividing both sides of the equation by 2, which gives you the following.
r = d / 2
This is the equation you can use to find the radius from the diameter of a circle. Consider a circle with a diameter of 20 centimeters. The calculation to find the circle's radius would look like this:
r = 20 cm / 2 = 10 cm
The calculation is the same no matter what the diameter. It's that simple.