From Latin: circus - "ring, a round arena"
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
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
||A point inside the circle. All points on the circle are equidistant (same distance) from the center point.
||The radius is the distance from the center to any point on the circle.
It is half the diameter.
See Radius of a circle.
||The distance across the circle. The length of any
chord passing through the center.
It is twice the radius. See Diameter of a circle.
||The circumference is the distance around the circle. See
Circumference of a Circle.
||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 .
||A line segment linking any two points on a circle. See
||A line passing a circle and touching it at just one point.
See Tangent definition
||A line that intersects a circle at two points.
See Secant definition
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
There are several definitions of a circle that you may come across. Below are some of the alternative ones.
"The set of all points equidistant from the center". This assumes that a line can be defined as an infinitely large set of points.
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. A similar definition to the one above.
(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
Equations of a circle
Angles in a circle
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