Definition of a circle

In geometry, a circle is the locus of points at the same distance from a given fixed point.

The word locus sounds complicated, but it means set of all points on a plane.

Another way then to define a circle is to say that it is the set of all points that are at the same distance from a fixed point.

All the blue dots are located at the distance from the red dot and they form the locus of points mentioned above.


You can put a great number of blue dots until you get a closed curved line figure.The following shows an example of circle:

Example of a circle

Real life examples of circles are bicycle wheels, coins, such as dimes and pennies, CDs, and MP3 players.

Lines on a circle are given different names depending on how the line cuts the circle.

A line segment joining two points on the figure is a chord. The following are examples of two chords.

Examples of chords

When a chord passes through the center, we call it a diameter. A diameter usually divides such figure into two equal halves. Each half is called a semi-circle

Example of a diameter

Half a diameter is called a radius. In other words, 2 radii = diameter

Example of a radius

A secant is shown in blue below. It is a line that intersects the circle in two points

Did you see the difference between the secant and the other lines? The secant is not contained within the circle. It is extended beyond the loci

Example of a secant

The tangent of a circle is shown in red. It is a line that touches the circle in exactly one point.

Tangent of a circle

Definition of a circle quiz. How well do you know basic facts about a circle?

Buy a comprehensive geometric formulas ebook. All geometric formulas are explained with well selected word problems.

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