Parts of a Circle
Learn about the centre, radius, and diameter of a circle
1. What is a Circle?
Definition
A circle is a closed curved shape where every point on the curve is the same distance from the centre.
A Circle with Centre O
Note: The centre is a point inside the circle. It is usually labelled with the letter O.
2. The Radius
Definition
The radius is a straight line from the centre of the circle to any point on the circle.
All radii (plural of radius) of the same circle have the same length.
Example: Circle with Radius 4 cm
The line from the centre O to the circle is a radius.
Symbol
We use r to represent the radius
All radii are equal
Every radius of this circle is 4 cm.
3. The Diameter
Definition
The diameter is a straight line that passes through the centre of the circle and has both endpoints on the circle.
The diameter is the longest straight line you can draw inside a circle.
Example: Circle with Diameter 10 cm
The line through the centre O, from one side of the circle to the other, is a diameter.
Symbol
We use d to represent the diameter
4. The Key Relationship: Diameter = 2 × Radius
The Formula
Diameter = 2 × Radius
or
d = 2 × r
This also means: Radius = Diameter ÷ 2 or r = d ÷ 2
Example 1: Finding Diameter from Radius
The radius of a circle is 5.5 m. Find its diameter.
Solution:
Radius = 5.5 m
Diameter = 2 × 5.5 m
Diameter = 11 m
Example 2: Finding Radius from Diameter
The diameter of a circle is 15 m. Find its radius.
Solution:
Diameter = 15 m
Radius = 15 m ÷ 2
Radius = 7.5 m
5. Practice Problems
Problem 1: Find the Diameter
The radius of a circle is 6 cm. Find its diameter.
ShowHide solution
Diameter = 2 × Radius
Diameter = 2 × 6 cm
Diameter = 12 cm
Problem 2: Find the Radius
The diameter of a circle is 24 cm. Find its radius.
ShowHide solution
Radius = Diameter ÷ 2
Radius = 24 cm ÷ 2
Radius = 12 cm
Problem 3: Missing Values
Complete the table:
| Circle | Radius | Diameter |
|---|---|---|
| W | 13 cm | ? |
| X | ? | 13 cm |
ShowHide solution
Circle W:
Diameter = 2 × 13 cm = 26 cm
Circle X:
Radius = 13 cm ÷ 2 = 6.5 cm
Key Takeaways
The centre (O) is the point inside the circle that is the same distance from every point on the circle.
The radius (r) is a line from the centre to any point on the circle.
The diameter (d) is a line passing through the centre with both endpoints on the circle.
Key formula: Diameter = 2 × Radius (or d = 2r)
All radii of the same circle are equal in length.