AQA · GCSE · Mathematics
Course version: 8300 · Version from Sept 2015
Identify and apply circle definitions and properties, including: centre,…
Full specification wording
Properties and constructions: identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference
A circle is the set of points at a fixed distance from a fixed point.
Checked against the AQA 8300 specification (opens in a new tab) on .
- Point 11 of 15
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A circle is the set of points at a fixed distance from a fixed point. The fixed point is the centre. The radius is any straight line segment from the centre to a point on the circle; all radii of the same circle are equal. A chord is a straight line segment joining two points on the circumference. The diameter is a chord that passes through the centre; it is the longest chord and equals twice the radius, so d = 2r. The circumference is the distance around the circle, given by C = 2πr or C = πd. For example, a circle with radius 5 cm has diameter 10 cm and circumference 10π cm. You must recognise these parts in a diagram and use the relationships to find missing lengths.
What earns the marks
- Define the centre as the fixed point equidistant from every point on the circle.
- Define the radius as a segment from the centre to the circumference and state that all radii are equal.
- Define a chord as a segment joining two points on the circumference, and the diameter as a chord through the centre.
- Use the relationship diameter = 2 × radius and radius = diameter ÷ 2.
- Apply the circumference formula C = 2πr or C = πd to calculate the distance around a circle.
Common mistakes and how to put them right
Calling any line across the circle a diameter.
Put it right: Only a chord that passes through the centre is a diameter.
Using the diameter in place of the radius in C = 2πr.
Put it right: Either halve the diameter first or use C = πd.
Thinking a chord must pass through the centre.
Put it right: A chord is any segment joining two points on the circumference, and the diameter is the special chord through the centre.
Confusing circumference with area.
Put it right: Circumference is the distance around the circle, measured in units such as cm, while area is measured in square units such as cm².
Exam tips
- Label the centre, radius, chord, diameter and circumference on any diagram before calculating.
- Check whether the question gives the radius or the diameter, and convert to the required form before substituting into a formula.
- Leave answers in terms of π when asked for an exact value, and only use a decimal approximation if the question requests it.
Try the lesson
The start of the Properties and constructions: identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference lesson, made from checked teaching notes for this specification point.
Have a go first
A circle has a diameter of 18 cm. What is the length of its radius?
Listen
A circle is the set of points at a fixed distance from a fixed point. The fixed point is the centre. The radius is any straight line segment from the centre to a point on the circle; all radii of the same circle are equal. A chord is a straight line segment joining two points on the circumference. The diameter is a chord that passes through the centre; it is the longest chord and equals twice the radius, so d = 2r. The circumference is the distance around the circle, given by C = 2πr or C = πd. For example, a circle with radius 5 cm has diameter 10 cm and circumference 10π cm. You must recognise these parts in a diagram and use the relationships to find missing lengths. A strong answer earns marks for these points. Define the centre as the fixed point equidistant from every point on the circle. Define the radius as a segment from the centre to the circumference and state that all radii are equal. Define a chord as a segment joining two points on the circumference, and the diameter as a chord through the centre. Use the relationship diameter = 2 × radius and radius = diameter ÷ 2. A common slip: Calling any line across the circle a diameter. Instead, only a chord that passes through the centre is a diameter. Exam tip: Label the centre, radius, chord, diameter and circumference on any diagram before calculating.
Key words
Say what each word means before you turn the card.
centre
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radius
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chord
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circumference
Try answering aloud or in your head before turning the card.
See every definition
- centre
- The fixed point from which every point on the circle is at a fixed distance.
- radius
- Any straight line segment from the centre to a point on the circle; all radii of the same circle are equal.
- chord
- A straight line segment joining two points on the circumference; the diameter is the special chord that passes through the centre.
- circumference
- The distance around the circle, given by C = 2πr or C = πd.
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