Circles Around Us Discover how roundness shapes our world.

What Is a Circle?

Circle

A circle is the set of points that are all the same distance from one fixed point called the centre.

Key Characteristics:

  • The fixed point is the centre.
  • Equal distance from the centre is the radius.
  • Smooth curved outline with no corners.

Example:

Think of a clock face or the top of a drum—both show a circle. Can you spot another one around you?

Center & Radius

Circle diagram

Identify Them Quickly

A circle is defined by its centre. The radius joins the centre to the curve.

Key Points:

  • Centre: fixed point exactly in the middle.
  • Radius: line segment joining centre to boundary.
  • All radii of one circle are equal in length.

Diameter Formula

\[d = 2r\]

Variable Definitions

\(d\) Diameter — straight line through centre, touches circle at two points.
\(r\) Radius — distance from centre to circle edge; half of diameter.

Applications

Find Diameter

If \(r = 5\; \text{cm}\), then \(d = 2 \times 5 = 10\; \text{cm}\).

Find Radius

If \(d = 18\; \text{cm}\), then \(r = \frac{18}{2} = 9\; \text{cm}\).

Label the Circle

Drag each label—Centre, Radius, Diameter—to its correct place on the circle.

Draggable Items

Centre
Radius
Diameter

Drop Zones

Drop here

Drop here

Drop here

Tip:

The radius stretches from the centre to the edge and is exactly half the diameter.

Circle Snapshot

A circle is the set of points equally distant from one centre.

Key parts: centre, radius, diameter.

Relationship: diameter \(= 2 \times\) radius.

Change the radius and the whole circle grows or shrinks.

Thank You!

We hope you found this lesson informative and engaging.