# Parts of a circle

Categories: gcse geometry

A circle is a curved shape. Every point on a circle is the same distance from the centre of the circle:

In this article, we will look at the parts of a circle. To learn about the areas and perimeters of circles, arcs, segments and sectors see Area and circumference of circles.

Here is a video:

## Radius of a circle

A radius of a circle is a line from the centre to any point on the edge of the circle. Since every point on the circle is an equal distance from the centre, you can draw a line from the centre in *any direction* and it will always form a radius.

The plural of radius is radii.

## Diameter of a circle

The diameter of a circle is any line drawn between two points on the circle that passes through the centre of the circle:

The diameter is formed by 2 radii, so the length of the diameter is twice the length of the radius.

## Circumference of a circle

The circumference of a circle is the length around the edge of the circle:

## How to find the circumference of a circle

The circumference of a circle with a radius *r* is given by this formula:

Where *l* is the circumference, *r* is the radius, and *pi* is a constant, equal to approximately 3.141592654.

The circumference of a circle with diameter *d* is given by this formula:

Where *d* is the diameter of the circle. This equation is true because the diameter is twice the radius.

## How to find the area of a circle

The area of a circle is given by the area formula of a circle:

## Secant to a circle

A secant is a straight line that cuts through a circle:

## Chord of a circle

A chord is a straight line between two points on the edge of the circle:

A chord is similar to a secant, except that the chord does not extend beyond the edge of the circle.

A diameter is a special chord that also passes through the centre of the circle.

## Tangent to a circle

A tangent is a straight line that just touches the circle:

## Segments, sectors and arcs of a circle

This diagram shows a segment, a sector, and an arc of a circle:

A sector is a "pie slice" of the circle. The angle *a* defines how big the pie slice is.

A segment is a part of the circle that is cut off by a chord. The angle *a* is the angle of the equivalent sector. We say that the segment *subtends* an angle *a* at the centre of the circle. This angle is sometimes called the central angle.

An arc is part of the circumference of the circle. Again, an arc subtends an angle *a* at the centre of the circle.

The areas and perimeters of arcs, segments and sectors are covered here.

## See also

- Tangent and radius of a circle meet at 90°
- Two radii form an isosceles triangle
- Perpendicular bisector of a chord
- Angle at the centre of a circle is twice the angle at the circumference
- Angle in a semicircle is 90 degrees
- Angles in the same segment of a circle are equal
- Opposite angles in a cyclic quadrilateral add up to 180°
- Two tangents from a point have equal length

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