Circle
A line forming a closed loop, every point on which is a fixed distance from a center point.
Try this Drag an orange dot. The circle can be moved by dragging the center point
and resized by dragging the point on the circle.
A circle is a type of line. Imagine a straight
line segment that is bent around until its ends join.
Then arrange that loop until it is exactly circular  that is, all points along that line are the same distance from a center point.
There is a difference between a circle and a disk. A circle is a line, and so, for example, has no area  just as a line has no area.
A disk however is a round portion of a
plane
which has a circular outline.
If you draw a circle on paper and cut it out, the round piece is a disk.
Properties of a circle
Center 
A point inside the circle. All points on the circle are equidistant (same distance) from the center point.

Radius 
The radius is the distance from the center to any point on the circle.
It is half the diameter.
See Radius of a circle.

Diameter 
The distance across the circle. The length of any
chord passing through the center.
It is twice the radius. See Diameter of a circle.

Circumference 
The circumference is the distance around the circle. See
Circumference of a Circle.

Area 
Strictly speaking a circle is a line, and so has no area.
What is usually meant is the area of the region enclosed by the circle.
See Area enclosed by a circle .

Chord 
A line segment linking any two points on a circle. See
Chord definition

Tangent 
A line passing a circle and touching it at just one point.
See Tangent definition

Secant 
A line that intersects a circle at two points.
See Secant definition

Calculator
Use the calculator on the right to calculate the properties of a circle.
Enter any single value and the other three will be calculated.
For example: enter the radius and press 'Calculate'. The area, diameter and circumference will be calculated.
Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference.
Pi
In any circle, if you divide the circumference (distance around the circle) by its diameter (distance across the circle),
you always get the same number. This number is called Pi and is approximately 3.142. See Definition of pi.
Relation to ellipse
A circle is actually a special case of an ellipse.
In an ellipse, if you make the major and minor axis the same length, the result is a circle, with both foci at the center.
See Ellipse definition
Circle as a conic section
You can define a circle as the shape created when a plane cuts through a cone at right angles to the cone's axis.
For more on this see
Conic sections  circle.
Circle as a locus
A circle is the locus
of all points a fixed distance from a given (center) point.
This definition assumes the plane is composed of an infinite number of points and we select only those
that are a fixed distance from the center.
(See locus definition.)
Equations of a circle
In coordinate geometry, a circle can be described using sets of equations.
For more on this see
Equations of circles and ellipses.
Other circle topics
General
Equations of a circle
Angles in a circle
Arcs
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