Circles are common shapes. You can see them everywhere—wheels on cars, compact discs with data, frisbees that pass through the air. All these things are circles.

Circles are \(2-dimensional\, figures\), just like quadrilaterals and polygons.

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However, a circle is measured differently than all the other shapes.

We even need to use a few different terms for describing them. Let’s look at these interesting shapes.

First: **Properties of Circles. **Circles represent sets of points that are all at the same distance from a fixed, central point.

We call this fixed, middle point the center. And the distance from the circle’s center to all points on our circle is what we call the radius.

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And when we put two radii (the plural form of radius) together and form one line segment across the entire circle, we have the diameter. Diameters of circles pass through the center point of our circle and have their endpoints on that circle itself.

So we see that a circle’s diameter is two \((2)\) times the circle’s radius’ length. We can represent that by the expression \(“2r”\), or \(“2\, times\, its\, radius”\). So if we know the radius of a circle, we multiply it by two \((2)\) and come up with its diameter. This also means that, if we know the diameter of a circle, we may divide by \(2\) (two) to discover its radius.

**For example:**

The problem: Find this circle’s diameter.

\(d = 2r\) The circle’s diameter is \(2\) (two) times its radius \((or \,2r\)).\(d = 2(7)\) This circle’s radius is seven \((7)\) inches.

\(d = 14\) So the diameter of our circle is \(2(7)\), or \(14\) inches.

The answer is: This the diameter of our circle is \(14\) inches.

**One more example:**

The Problem: Find this circle’s radius.

\(\begin{align*} r&=\frac{1}{2}\,d\\ \\r&=\frac{1}{2}\,(36)\\ \\r&=18 \end{align*} \)

The circle’s radius is half its diameter, or \(\frac{1}{2}\,d \).

This circle’s diameter is \(36\) feet, so its radius is \(\frac{1}{2}\,(36) = 18\) feet.

The answer is:

The circle’s radius is \(18\) feet.