Radius
Line from the centre to the circumference.
Learning Objectives
- name the main parts of a circle;
- distinguish between arcs, sectors and segments;
- recognise tangents and secants;
- use radius and diameter relationships;
- label circle diagrams accurately.
Introduction
This lesson develops Parts of a Circle from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Parts of a Circle
Key Vocabulary
Diameter
Chord through the centre; twice the radius.
Chord
Line joining two points on the circumference.
Arc
Part of the circumference.
Sector
Region between two radii and an arc.
Segment
Region between a chord and an arc.
Tangent
Line touching the circle at one point.
Secant
Line crossing a circle at two points.
Important Relationships
Diameter = 2 ร radius
A sector is shaped like a slice of pizza. A segment is cut off by a chord.
Try It: Radius, Diameter and Circumference
๐ง Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- Define radius, diameter and chord.
- A circle has radius 7 cm. Find its diameter.
- A diameter is 18 cm. Find the radius.
- Explain the difference between a sector and a segment.
- What is special about a tangent at the point of contact?
โ Check Your Work
Show answers and working
- Radius: centre to circumference. Diameter: chord through centre. Chord: joins two circumference points.
- 14 cm.
- 9 cm.
- A sector lies between two radii and an arc; a segment lies between a chord and an arc.
- The radius to the point of contact is perpendicular to the tangent.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- d=2r.
- A tangent touches once; a secant crosses twice.
- A diameter is the longest chord.