Circles: Definition, Parts of Circle, Formulas and Examples

Circle, Formulas

A circle is a special type of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also referred to as the locus of points drawn equidistant from the centre. The radius of a circle is the distance between its centre and a point on the circle. Diameter, also known as the longest chord of a circle, is the line that splits a circle into two equal halves and is equal to twice the radius.

The circle is a two-dimensional figure with an area and a perimeter. The perimeter of the circle is also called the circumference of a circle, which is the length of the boundary of the circle. The area of a circle is the region enclosed by it.

Let’s learn about circle definitions, formulas and important terms with examples in detail.

Circle Definition

A circle is a two-dimensional figure made up of the locus of all points present at the same distance (radius) from a fixed point (centre). The fixed point is referred to as the circle’s origin or centre, and the fixed distance between each point and the origin is referred to as the radius.

There are numerous circular items that you must have encountered in daily life. Some examples are rings, coins, wheels and so on.

Parts of Circle

A circle comprises parts based on their positions and properties. The various parts of a circle are explained in depth below.

Annulus-The area defined by two concentric circles. It’s basically a ring-shaped object.

Arc – It is basically a part of a circle.

Sector – A area enclosed by two radii and an arc.

Segment- A area enclosed by a chord and an arc. It should be noted that segments do not contain the centre.

Centre – The midpoint of a circle.

Chord- A line segment that connects two distant points on a circle.

Diameter- The largest chord of the circle that passes through the centre.

Radius- A line segment that connects any point on the circle to its centre.

Secant- A straight line with two distinct points on the circle where it intersects the circle. It’s also known as an extended chord.

Tangent- A straight line that touches the circle at only a single point.

Radius of Circle (r)

A line segment that joins the centre of the circle to any point on the circle. The radius of a circle is represented by the letters “R” or “r.”

Diameter (d) of Circle

A line segment with endpoints on the circle passes through the centre. It is twice the radius length, d = 2r. The radius of the circle is calculated as r= d/2 from the diameter.

Circle Formulas

A circle is a two-dimensional curve-shaped figure, and the two parameters used to measure the circle are:

  • Area of  circle
  • Circumference of a circle

Circumference of a circle

The distance around a circle is defined as its circumference. The phrase ‘perimeter’ is also sometimes used, however, this usually refers to the distance surrounding polygons, figures made up of the straight line segment.

The circumference of a circle (C) = ?d = 2 ? r

Where, ? = 3.1415 or 22/7

Area of  circle

A circle’s area is the amount of space it encloses.

Area of a circle = ?r2

Properties of Circles

The following are the basic properties of circles:

  • Every point on the circle is at the same distance from the centre of the circle.
  • The circle’s diameter divides it into two equal parts.
  • Circles with equal radii are congruent to one another.
  • Circles of varied sizes and radii are similar.
  • The circle’s diameter is the largest chord and is twice the radius.