Definition:Circle

Definition



 * Circle.png

Center


(Note: UK English spells this centre.)

In the above diagram, the center is the point $A$.

Circumference
The circumference of a circle is the line that forms its boundary.

It is also often taken to refer to the length of this line.

Diameter


In the above diagram, the line $CD$ is a diameter.

Radius
A radius (plural radii, pronounced ray-dee-eye) of a circle is a straight line segment whose endpoints are the center and the circumference of the circle.

In the above diagram, the line $AB$ is a radius.

Arc
An arc of a circle is any part of its circumference.

Sector
A sector of a circle is the area bounded by two radii and an arc.



In the above diagram, $ABC$ is a sector.


 * Sector.png

In fact there are two sectors, together making up the whole of the circle.

Chord
A chord of a circle is a straight line segment whose endpoints are the circumference of the circle.

In the diagram at the top of the page, the lines $CD$ and $EF$ are both chords.

Note that under this definition, the diameter itself is in fact a chord.



Equally Distant from the Center




Area
It can be shown that the area of a circle is $\pi r^2$, where $r$ is the radius.

Equation
It can be shown that the equation of a circle in Cartesian coordinates is $x^2 + y^2 = R^2$, in polar coordinates is $r \left({\theta}\right) = R$, and parametrically by $x = R \cos t, y = R \sin t$.