Cambridge Primary Checkpoint · Mathematics · Stage 6 · Geometry and Measure
Circles: Parts and Constructing Circles
Learn the centre, radius, diameter and circumference of a circle, and how to construct a circle of any radius or diameter with compasses.
British & IGCSE › Checkpoint 6 › Checkpoint 6 Maths — Complete Course
- Know and name the parts of a circle: centre, radius, diameter and circumference. [6Gg.02]
- Use a pair of compasses to construct (draw accurately) a circle with a given radius or a given diameter. [6Gg.11]
A circle is the set of all points that are the same distance from one fixed point, the centre. That one idea explains everything on this page: why every radius is the same length, why the diameter is twice the radius, and how a pair of compasses draws a perfect circle.
1. Key words
| Word / phrase | Meaning / use |
|---|---|
| circle | دائرة — a round 2D shape; every point on it is the same distance from the centre |
| centre | المركز — the point in the exact middle of the circle |
| radius (plural radii) | نصف القطر — a straight line from the centre to the circumference; also its length |
| diameter | القطر — a straight line from one side of the circle to the other, passing through the centre |
| circumference | المحيط — the curved line all the way round the circle; also its length (the perimeter of the circle) |
| pair of compasses | البرجل — the instrument used to draw circles |
| construct | يرسم بدقة — draw accurately with a ruler and compasses |
| chord | وتر — a straight line joining two points on the circumference (a diameter is the longest chord) |
2. The parts of a circle
| Part | What it is | How to recognise it |
|---|---|---|
| centre | the middle point | often a dot, labelled O or C |
| radius | centre → circumference | starts at the centre, stops at the edge |
| diameter | edge → centre → edge | goes right across and passes through the centre |
| circumference | the distance around | the curved outline itself, not a straight line |
Two facts that follow from the definition:
- All the radii of one circle are the same length, and all its diameters are the same length.
- A diameter is made of two radii in a straight line, so diameter = 2 × radius and radius = diameter ÷ 2.
A straight line that joins two points on the circle but does NOT pass through the centre is a chord, not a diameter. It is always shorter than the diameter. A line through the centre that does not reach the circumference at both ends is not a diameter either.
- نصف القطر (radius): من المركز للمحيط. القطر (diameter): من المحيط للمحيط ويعدّي بالمركز.
- القطر = 2 × نصف القطر، ونصف القطر = القطر ÷ 2.
- المحيط (circumference): الخط المنحني اللي حوالين الدائرة كلها، مش خط مستقيم.
3. Constructing a circle with a pair of compasses
To construct a circle with a given radius (for example 3 cm):
- Check the pencil in the compasses is sharp and its tip is level with the point (needle).
- Put the point exactly on the 0 mark of your ruler and open the compasses until the pencil tip is exactly on 3 cm.
- Mark the centre with a small dot (or use the centre given in the question). Put the point on it and press gently so it does not slip.
- Hold the compasses by the top handle only and turn them all the way round in one smooth movement. Do not change the width while you turn.
- Check: measure from the centre to the circle in two or three places — each should be 3 cm.
To construct a circle with a given diameter (for example 7 cm): first halve the diameter to find the radius: 7 ÷ 2 = 3.5 cm. Then set the compasses to 3.5 cm and follow the same steps. Check by drawing a straight line through the centre from one side to the other — it should measure 7 cm.
Drawing circle patterns. Many questions ask you to copy a pattern of circles, for example two circles of radius 3 cm whose centres are 3 cm apart, so each circle passes through the other's centre. Draw a line, mark the two centres with the ruler, then draw each circle with the compasses set to the radius.
- Use a sharp HB pencil — thick lines make your radius inaccurate.
- Never rub out the centre point; examiners look for it.
- If the question says "diameter", halve it before setting your compasses.
- Keep construction marks; they show your method.
4. Worked examples
Worked example 1 (1 mark) A circle has a radius of 8.5 cm. What is its diameter?
- diameter = 2 × radius
- 2 × 8.5 = 17
- Answer: 17 cm.
Common mistake: halving instead of doubling (4.25 cm). Ask yourself: is the diameter longer or shorter than the radius? Longer — so multiply.
Worked example 2 (1 mark) The diameter of a coin is 2.6 cm. What is its radius?
- radius = diameter ÷ 2
- 2.6 ÷ 2 = 1.3
- Answer: 1.3 cm.
Worked example 3 (1 mark) Two identical circles fit exactly inside a rectangle 20 cm long and 10 cm wide. Each circle touches the other circle and the sides of the rectangle. Find the radius of one circle.
- Across the length there are 2 diameters: 20 ÷ 2 = 10 cm, so each diameter is 10 cm.
- Check with the width: one diameter fits the 10 cm width. ✓
- radius = 10 ÷ 2 = 5 cm.
- Answer: 5 cm.
Common mistake: dividing 20 by 4 straight away without thinking, or giving the diameter (10 cm) when the question asks for the radius. Underline the word radius or diameter in the question.
Worked example 4 (2 marks) Construct a circle with diameter 9 cm. Draw and label one radius.
- Radius = 9 ÷ 2 = 4.5 cm.
- Set the compasses to 4.5 cm on a ruler, mark a centre, and draw the circle.
- Draw a straight line from the centre to the circle and label it "radius".
- Marking: 1 mark for a circle with diameter 9 cm (drawn accurately), 1 mark for a correctly drawn and labelled radius.
Worked example 5 (1 mark) Circle P has a radius of 4 cm. Circle Q has a diameter that is 3 times the diameter of circle P. What is the radius of circle Q?
- Diameter of P = 2 × 4 = 8 cm.
- Diameter of Q = 3 × 8 = 24 cm.
- Radius of Q = 24 ÷ 2 = 12 cm.
- Answer: 12 cm. (Shortcut: if the diameter is 3 times bigger, the radius is also 3 times bigger: 3 × 4 = 12 cm.)
Worked example 6 (2 marks) Two circles have the same centre. The large circle has a diameter of 18 cm. The small circle has a radius of 5 cm. How wide is the ring between the two circles (measured along a radius)?
- Change everything to radii: large radius = 18 ÷ 2 = 9 cm.
- Small radius = 5 cm.
- Width of the ring = 9 − 5 = 4 cm.
- Answer: 4 cm. Marks: 1 mark for finding the radius 9 cm (or a method 18 ÷ 2 − 5), 1 mark for 4 cm.
Common mistake: working out 18 − 5 = 13 cm, which mixes a diameter with a radius. Always compare like with like — radius with radius, or diameter with diameter.
- Mixing up radius and diameter. Radius → from the centre; diameter → right across through the centre.
- Setting the compasses to the diameter when the question gives a diameter. Halve it first.
- Calling any line across a circle a diameter. It must pass through the centre.
- Thinking the circumference is a straight line or a point. It is the whole curved edge (the distance around).
- Letting the compasses slip or open wider while turning: hold them by the top only.
- Forgetting units (cm) or giving the radius when the diameter was asked for.
- Label the parts: draw lines from the words centre, radius, diameter, circumference to a diagram, or name a line marked on a circle.
- Find a radius or diameter from a picture of circles inside a rectangle or square, or touching each other in a row. Count how many diameters fit across.
- Construct a circle of a given radius or diameter with compasses — sometimes on a given centre or inside a box. Accuracy matters.
- Complete a sentence: "The diameter is ___ times the length of the radius."
- "Explain" or "Tick the correct statement" questions on the relationship between radius and diameter.
Practice
- Centre = the middle point. Radius = centre to edge. Diameter = edge to edge through the centre. Circumference = the distance all the way round.
- diameter = 2 × radius; radius = diameter ÷ 2.
- All radii of a circle are equal; all diameters are equal.
- Compasses are always set to the RADIUS — halve a diameter first.
- For circles in a row or inside a square, count how many diameters fit across.
All pages in this course
Start here
Number: integers and calculation
- Counting On and Back and Negative Numbers
- Sequences, Letters and Position-to-Term Rules
- Order of Operations, Brackets and Laws of Arithmetic
- Multiplying Whole Numbers (up to 10 000 × 2-digit)
- Dividing Whole Numbers (up to 1000 ÷ 2-digit)
- Factors, Multiples and Tests of Divisibility
- Square Numbers and Cube Numbers
Number: place value, decimals, fractions, percentages and ratio
- Place Value and Decimals to Thousandths
- Rounding Decimals
- Fractions: Division, Operators and Simplest Form
- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions by Whole Numbers
- Fractions, Decimals and Percentages: Equivalence and Ordering
- Adding, Subtracting, Multiplying and Dividing Decimals
- Ratio and Direct Proportion
Geometry and measure
- Time: Decimals and Mixed Units
- Quadrilaterals: Properties and Classification
- Circles: Parts and Constructing Circles
- Angles: Measuring, Drawing and Angles in a Triangle
- Area of Rectangles and Right-angled Triangles
- 3D Shapes, Compound Shapes and Nets
- Capacity, Volume and Surface Area
- Coordinates in Four Quadrants
- Rotational Symmetry, Translation, Reflection and Rotation
Statistics and probability
Practice tests