2D shapes
Circles
A circle is a set of points that are all the same distance from a middle point called the centre. In this topic you learn the names of the parts of a circle and how the radius and diameter are connected.
The parts of a circle
• Centre: the point in the exact middle of the circle. • Radius: the distance from the centre to any point on the circle. Every point on the circle is the same distance (the radius) from the centre. The plural of radius is radii. • Circumference: the perimeter — the curved distance all the way around the circle. • Diameter: a straight line joining two points on the circle that passes through the centre.
Radius and diameter
The diameter goes right across the circle through the centre, so it is made of two radii joined together. This gives two rules: • diameter = 2 × radius • radius = diameter ÷ 2 Remember that 1 cm = 10 mm, so a radius of 3 cm is the same as a radius of 30 mm.
Drawing circles with compasses
To draw a circle you open your compasses to the radius, mark the centre with a dot, place the point on the dot and turn the compasses carefully. Opening the compasses to 4 cm draws a circle of radius 4 cm (and diameter 8 cm).
Touching circles
When two circles just touch, the distance between their centres is the two radii added together. For example, a circle of radius 6 cm touching a circle of radius 2.5 cm has centres 6 + 2.5 = 8.5 cm apart.
Worked examples
Naming a part of the circle
- Chris ran in a straight line from one side of a circular lawn, through the centre, to the other side.
- A straight line through the centre joining two points on the circle is the diameter.
Answer: Chris ran along the diameter.
Diameter from the radius
- A circle has a radius of 3 cm.
- The diameter is two radii: diameter = 2 × radius.
- Work out 2 × 3.
Answer: The diameter is 6 cm.
Radius from the diameter
- A circle has a diameter of 8 cm.
- The radius is half the diameter: radius = diameter ÷ 2.
- Work out 8 ÷ 2.
Answer: The radius is 4 cm.
Are two circles the same size?
- Arun draws a circle of radius 3 cm. Sofia draws a circle of diameter 60 mm.
- Radius 3 cm = 30 mm, so Arun's diameter is 2 × 30 = 60 mm.
- Both circles have a diameter of 60 mm.
Answer: Yes — both circles are the same size.
Distance between two touching circles
- Circle A has radius 6 cm and circle B has radius 2.5 cm, and they touch.
- The distance between the centres is the sum of the radii: 6 + 2.5.
- Add the two radii together.
Answer: The centres are 8.5 cm apart.
Where you see this in real life
- Using a pair of compasses to draw a circle of a chosen radius.
- Running around the edge of a circular lawn follows the circumference.
- Two coins placed so they just touch: the gap between their centres is the sum of their radii.
Key words
- Centre
- The point in the exact middle of a circle.
- Radius
- The distance from the centre to a point on the circle (plural: radii).
- Diameter
- A straight line across a circle through the centre; it is twice the radius.
- Circumference
- The perimeter — the distance all the way around a circle.
- Compasses
- A tool used to draw circles accurately.