# ##\$ Diameter of a Circle

## What is the Diameter of a Circle?

The diameter of a circle is a chord that passes through the center of the circle.

The word comes from the Greek word “diametros” which comes from two root words.

The root word “dia” means “across” or “through”. And root word “metron” means “measure”.

Ancient mathematicians chose this word because the diameter of a circle measures the distance across a circle.

## Diameter and Radius

The radius of a circle is the distance from the center of a circle to the circumference. Because the diameter is a straight line that goes through the center of a circle, it is basically two radii stuck together.

If you are given the diameter and you need to find the radius, you can split the diameter in half.

If you are given the radius and you need to find the diameter, you can double the radius.

## Examples

What is the diameter?

The radius is $$\green 5\,m$$ and the diameter is always twice as long as the radius.

$2\times5=10$

So, the diameter is $$\green 10\,m$$.

What is the radius?

The diameter is $$\blue 3\, ft$$ and the radius is always half as long as the diameter.

$3\div2=1.5$

So, the radius is $$\blue 1.5\,ft$$.

## When Will I Use the Diameter of a Circle?

When you calculate the circumference of a circle, you will plug the diameter measurement into the circumference formula.

When you calculate the circumference of a circle, you will plug the diameter measurement into the area formula.

The diameter always cuts the circle exactly in half, which is why it is easy to find the area of a semicircle.

An inscribed angle that subtends the diameter will always equal $$90^\circ$$ because of the Inscribed Angles Theorem.