The circle and the disc
Definitions: circle, disc, radius and diameter
The circle
A circle with centre O and radius r is the set of all points lying exactly at a distance r from the point O. In other words, all points on the circle are the same distance from the centre.
Beware of the classic pitfall: a circle is just a line (the outline), not the area inside it!
The disc
A disc with centre O and radius r is the set of points lying at a distance less than or equal to r from the point O. The disc is the circle AND the entire interior (the solid area).
| Object | What it is | Example |
|---|---|---|
| Circle | The curved line (the edge) | The outline of a coin |
| Disc | The solid area | The whole coin |
Radius and diameter
The radius (denoted by r) connects the centre O to any point on the circle.
The diameter (denoted by d) is a line segment that passes through the centre O. It connects two opposite points on the circle.
Fundamental relationship: d = 2 × r (and therefore r = d / 2).
Example
If a circle has a radius r = 5 cm, then its diameter is d = 2 × 5 = 10 cm.
If a disc has a diameter d = 14 cm, then its radius is r = 14 / 2 = 7 cm.
Additional vocabulary
- A chord is a line segment connecting two points on the circle (the diameter is the longest possible chord).
- An arc is a portion of a circle bounded by two points.
Making a clear distinction between a circle and a disc helps to avoid many mistakes in exercises involving circumference and area, which will be covered in the next lesson.