CIRCLES

Definition: A circle is a shape with all points the same distance from its center. A circle is named by its center. Some real world examples of a circle are a wheel, a dinner plate and (the surface of) a coin.                                                               

 Radius, Diameter and Circumference

The Radius is the distance from the center to the edge.

The Diameter starts at one side of the circle, goes through the center and ends on the other side.

The Circumference is the distance around the edge of the circle.

And here is the really cool thing:

So when the diameter is 1, the circumference is 3.141592654...

We can say:

Circumference = π � Diameter

Example: A man walks around the center circle of a football field, which has a diameter of 100m, how far has he walked?

Distance walked = Circumference = π � 100m = 314m (to the nearest m)

Also note that the Diameter is twice the Radius:

Diameter = 2 � Radius

And so this is also true:

Circumference = 2 � π � Radius

Remembering

The length of the words may help you remember:

• Radius is the shortest word
• Diameter is longer (and is 2 � Radius)
• Circumference is the longest (and is π � Diameter)

Area

The area of a circle is π times the radius squared, which is written:

A = π � r²

Or, in terms of the Diameter:

A = (π/4) � D²

Names

Because people have studied circles for thousands of years special names have come about.

Nobody wants to say "that line that starts at one side of the circle, goes through the center and ends on the other side" when a word like "Diameter" would do.

So here are the most common special names:

Lines A line that goes from one point to another on the circle's circumference is called a Chord. If that line passes through the center it is called a Diameter. A line that "just touches" the circle as it passes by is called a Tangent. And a part of the circumference is called an Arc.