Watch out
Using the full chord in the right-angled triangle.
Scottish National 5 Mathematics
National 5 Maths Circle geometry
Use the relationship between a circle's centre, a chord and its perpendicular bisector.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Mark the midpoint of the chord created by the perpendicular.
- Decide whether a calculator supports the method; exact working may still be required.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Circle geometry is an assessed part of Scottish National 5 Mathematics in the geometry area. Use the relationship between a circle's centre, a chord and its perpendicular bisector.
Mark the midpoint of the chord created by the perpendicular.
Use the radius, half-chord and centre distance as a right-angled triangle.
Apply Pythagoras or angle facts as required.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- A perpendicular from the centre of a circle to a chord bisects the chord.
Check
The perpendicular from the centre must meet the chord at 90° and split it into two equal lengths.
Exam tip
Mark the diagram with the values you use, show the formula and finish with the correct length, area or volume units.
Worked examples
Worked example 1
Circle geometry worked example
A chord of length 16 cm is 6 cm from the centre. Find the radius.
- The perpendicular bisects the chord, so half is 8 cm.
- r² = 6² + 8² = 100
Answer: 10 cm
Watch out
- Using the full chord in the right-angled triangle.
- Assuming a line bisects a chord without the perpendicular-centre condition.