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# Circles and Circumference Study Guide

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Updated on Oct 3, 2011

## Introduction to Circles and Circumference

It is easier to square a circle than to get round a mathematician.

—Augustus de Morgan (1806–1871)

You've undoubtedly come across the circle in your lifetime. But how well do you really know this shape? This lesson will teach you the parts of a circle and expose you to the circle's accomplice—pi.

A Circle is a closed figure in which each point of the circle is the same distance from the center of the circle.

A chord is a line segment that joins two points on a circle.

A radius is a line segment from the center of the circle to a point on the circle. You can name a radius by its points.

A diameter is a chord that passes through the center of the circle and has endpoints on the circle. You can name a diameter by its points.

An arc is a curved line that makes up part or all of a circle. If a circle is comprised of two arcs, the larger arc is called the major arc, and the smaller arc is called the minor arc.

A minor arc is the smaller curve between two points.

A major arc is the larger curve between two points

## Measuring a Circle

When you measure the distance around a circle, the distance is called a circumference. Think of circumference and circles the same way you think of quadrilaterals and perimeter: They are both measures of the distance around the outside.

As you learned in Lesson 20, when you deal with circles and circumference, you deal with a circle's partner pi, which is also represented by the symbol π. Pi is the ratio between the circumference of a circle and its diameter. It is equal to about 3.14, or .

#### Tip:

On most math tests, you will be advised to use π or one of the approximate values of π: 3.14, or . Pay close attention to which one you are told to work with.

 For the circumference of a circle, C, use one of the following formulas: C = 2πr, which translates to pi times twice the radius C = πd, which translates to pi times the diameter

Notice that both of these formulas are correct because the diameter is twice the radius. In other words, 2r = d.

Let's look at an example.

The circumference of this circle is 8π because the diameter is 8. Try another. But use 3.14 for pi.

The radius is 5, so plug this into the circumference formula:

C = 2π5

You know that 2 times 5 is 10, so you can simplify the expression to 10π. But you haven't finished just yet. You were told to use 3.14 for pi. Plug in that value:

C = 10π
C = 10 × 3.14
C = 31.4

The circumference is 31.4 inches.

Find practice problems and solutions for these concepts at Circles and Circumference Practice Questions.

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