All About Circles Discover the magic of every perfect round!

Circle Meaning

Circle

A circle is a closed, perfectly round curve. Every point on the curve is the same distance from one fixed point, the centre.

Centre Point

Centre of a Circle

The centre is the single point exactly in the middle of the circle. Every point on the circle is the same distance from it.

Key Characteristics:

  • Unique—each circle has only one centre.
  • Line from centre to circle forms a radius.

Try it:

Tap the dot that is equally distant from the circle’s edge to find the centre.

Radius

Radius

A radius is a line segment that connects the centre of a circle to any point on its circumference.

Key Characteristics:

  • Half of the diameter.
  • Equal length everywhere on the circle.
  • Infinitely many radii in one circle.

Example:

A wheel with a 10 cm diameter has a radius of 5 cm.

Diameter

Diameter

A diameter is a straight line segment that passes through the centre of a circle and joins two opposite points on the circle.

Key Characteristics:

  • Always passes through the centre.
  • Connects two points on the circle.
  • Longest chord of the circle.
  • Length is twice the radius.

Example:

If the radius of a circle is 3 cm, its diameter is 6 cm.

d = 2r

\[d = 2r\]

Variable Definitions

r radius – distance from centre to circle
d diameter – full width through centre

Applications

Key Idea

Use the relation to switch between radius and diameter quickly.

Example

If \(r = 3\text{ cm}\), then \(d = 6\text{ cm}\).

Try Now

Fill in the blank: If \(r = 5\text{ cm}\), \(d = \_\_ \text{ cm}\).

Circumference

Circumference

The circumference is the total distance around a circle, like the line that marks a round running track.

Key Characteristics:

  • It is the circle’s perimeter.
  • Measured in units of length (cm, m, etc.).
  • Every point on it is equally distant from the centre.

Example:

If the edge of a round track is 400 m long, that 400 m is its circumference.

Circle Recap

Center

The fixed point from which every point on the circle is equally distant.

Radius

Line from the center to any point on the circle; all radii are equal.

Diameter

Longest chord passing through the center; \( \text{Diameter} = 2 \times \text{Radius} \).

Circumference

Perimeter of the circle; \( C = 2\pi r \).