# Circle

A circle is easy to make:
And so: All points are the same distance from the center. |

## You Can Draw It Yourself

Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!

## Play With It

Try dragging the point to see how the radius and circumference change.

(See if you can keep a constant radius!)

## Radius, Diameter and Circumference

The **Radius** is the distance from the center outwards.

The **Diameter** goes straight across the circle, through the center.

The **Circumference** is the distance once around the circle.

And here is the really cool thing:

When we divide the circumference by the diameter we get 3.14159265...

which is the number π (Pi)

So when the diameter is 1, the circumference is 3.14159265... |

We can say:

Circumference = **π** × Diameter

### Example: You walk around a circle which has a diameter of 100m, how far have you 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

In Summary:

× 2 |
× π |

Radius | Diameter | Circumference |

## Remembering

The length of the words may help you remember:

**Radius**is the shortest word and shortest measure**Diameter**is longer**Circumference**is the longest

## Definition

The circle is a plane shape (two dimensional), so: |

**Circle**: the set of all points on a plane that are a fixed distance from a center.

## Area

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

A = **π** r^{2}

Where

**A**is the Area**r**is the radius

To help you remember think "Pie Are Squared" (even though pies are usually round):

### Example: What is the area of a circle with radius of 1.2 m ?

^{2}

^{2}

**4.52**(to 2 decimals)

Or, using the Diameter:

A = (**π**/4) × D^{2}

### Area Compared to a Square

A circle has **about 80%** of the area of a similar-width square.

The actual value is (π/4) = 0.785398... = 78.5398...%

And something interesting for you to try: Circle Area by Lines

## 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 they can just say "Diameter".

So here are the most common special names:

## Lines

A line that "just touches" the circle as it passes by is called a **Tangent**.

A line that cuts the circle at two points is called a **Secant**.

A line segment that goes from one point to another on the circle's circumference is called a **Chord**.

If it passes through the center it is called a **Diameter**.

And a part of the circumference is called an **Arc**.

## Slices

There are two main "slices" of a circle.

The "pizza" slice is called a Sector.

And the slice made by a chord is called a Segment.

## Quadrant

The Quadrant is a special sector with a right angle. It has a quarter of the circle's area.

## Semicircle

Half a circle is called a **Semicircle.**

## Inside and Outside

A circle has an inside and an outside (of course!). But it also has an "on", because we could be right on the circle.

Example: "A" is outside the circle, "B" is inside the circle and "C" is on the circle.

### Ellipse

A circle is a "special case" of an ellipse.