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Definition of a circle

A circle is the path traced out by a point, moving in a plane, that is always a fixed distance (the radius) from a fixed point (the centre).

Circle with centre labelled 'O' and 'centre'. Radius drawn and labelled 'radius'

Parts of the circle

Any interval (or line segment) drawn from the centre of a given circle to any point on the circle is called a radius (plural radii).

Any interval joining two points on the circle and passing through the centre is called the diameter of the circle.

Two circles, both with centre labelled 'O'.
Detailed description

Because every radius has the same length and every diameter has the same length, we often use the words 'radius' and 'diameter' to refer to either the interval in question or the length of that interval. Thus the diameter of a circle is twice the radius of that circle.

A diameter divides the circle into two congruent parts. Each part is called a semicircle. If we draw a radius perpendicular to the diameter in a semicircle, we obtain two congruent quadrants.

One semicircle labelled 'semicircle'; one quarter circle labelled 'quadrant'

Any two radii divide the circle into two pieces. Each piece is called a sector (from the Latin word secare − to cut).

One circle cut into two sectors, each labelled 'sector' and the centre labelled 'O'

Features of the circle