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GCSE Maths Geometry and Measure

Circles, Sectors and Arcs

Parts of a circle

Parts of a Circle

Here we will learn about the different parts of a circle including how to identify the key parts of a circle from a diagram, how to identify the key parts of a circle from a definition and how to draw a circle with the different parts labelled e.g. the diameter of a circle.

There are also parts of a circle worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are the parts of a circle?

The parts of a circle are the circle, centre, radius, diameter, circumference, arc, area, chord, secant, tangent, sector and segment.

parts of a circle image

Circle

A round plane figure whose boundary consists of points equidistant from a fixed point.

Centre

The centre of the circle is the fixed point from which all points on the boundary of the circle are equidistant.

Often noted on diagrams as ‘O’.

Parts of a Circle image 1 1

Centre/center are the same. Centre is the UK spelling whilst Center is the US spelling.

Radius

The distance from the centre of a circle to the outside.

The radius of the circle is half the diameter of the circle.

The plural of radius is radii.

Diameter

The distance across the circle going through the centre.

The diameter is twice the radius.

Parts of a Circle image 2 1

Circumference

The distance once around the circle.

Parts of a Circle image 3 1

Arc

A part of the circumference.

Parts of a Circle image 4 1

Major arc – A major arc is greater than half the circumference.

Minor arc – A minor arc is less than half the circumference.

Area

The space inside a 2D shape.

Chord

A line segment going from one point of the circumference to another but does not go through the centre.

Secant

A line that goes through the circle at two points.

Parts of a Circle image 5 1

Note: Secant is not a term you are required to know at GCSE, however it is important to note the difference between a chord and a secant.

Tangent

A straight line that touches the circle at a single point only.

Parts of a Circle image 6 1

Sector

A section of the circle created by two radii.

Major sector – A major sector has a central angle which is more than 180^o .

Minor sector – A minor sector has a central angle which is less than 180^o .

Parts of a Circle image 7 1

Semi circle

Half of a circle. Could be considered a sector where the circle has be split by the diameter.

Quadrant

A quarter of a circle, created by two perpendicular radii.

Parts of a Circle image 8 1

Segment

A section of the circle created by a chord.

Parts of a Circle image 9 1

Major segment – a segment where the arc is greater than half the circumference.

Minor segment – a segment where the arc is less than half the circumference.

Parts of a Circle image 10 1

What are the parts of a circle?

What are the parts of a circle?

Other keys terms:

Equidistance

A point is equidistant from 2 other points when it is always the same distance away from those points.

Angles around a point

Angles around a point are equal to 360^o .

How to identify parts of a circle

In order to identify/label parts of a circle:

1 Identify the key aspects of the part of the circle.

  • Is it a line or part of the circle’s area?
  • If a line goes through the origin of the circle?
  • If a line, is it part of the circle’s circumference?
  • If part of the circle’s area is it a segment or sector?

2 Clearly state your answer, consider whether the part of a circle you have identified has a specific name e.g. semicircle, major segment.

Explain how to identify parts of a circle

Explain how to identify parts of a circle

Parts of a circle worksheet

Get your free parts of a circle worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Parts of a circle worksheet

Get your free parts of a circle worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON

Parts of a circle examples

Example 1: identifying a part of a circle from a diagram

Name the part of the circle shown in red in the below diagram.

Parts of a Circle Example 1 1

  1.  Identify the key aspects of the part of the circle. Here are some key questions you can ask yourself?

  • Is it a line or part of the circle’s area?                          Line
  • If a line goes through the origin of the circle?             Yes
  • If a line, is it part of the circle’s circumference?            No

2Clearly state your answer, consider whether the part of a circle you have identified has a specific name e.g. major segment.

Radius

Example 2: identifying a part of a circle from a diagram

Name the part of the circle shown in red in the below diagram.

Parts of a Circle Example 2 1

  • Is it a line or part of the circle’s area?      Part of the area
  • If part of the circle’s area is it a segment or sector?      Sector as the radii meet at the origin

Sector – specifically the minor sector.

Example 3: identifying a part of a circle from a diagram

Parts of a Circle Example 3 1

  • Is it a line or part of the circle’s area?                          Line
  • If a line goes through the origin of the circle?             No
  • If a line, is it part of the circle’s circumference?           No

Chord

Example 4: identifying a part of a circle from a diagram

Name the part of the circle shown in red in the below diagram.

Parts of a Circle Example 4 1

  • Is it a line or part of the circle’s area?      Part of the area
  • If part of the circle’s area is it a segment or sector?      Sector as the radii meet at the origin

Sector – specifically the minor sector.

Example 5: identifying a part of a circle from a diagram

Parts of a Circle Example 5 1

  • Is it a line or part of the circle’s area?                          Line
  • If a line goes through the origin of the circle?             No
  • If a line, is it part of the circle’s circumference?           No, it touches the circumference of the circle at one point

Tangent

Example 6: labelling a part of a circle on a diagram

On the circle below:

Draw a diameter.

Draw a tangent.

Label the circumference.

Parts of a Circle Example 6 1

Here you are being asked to draw the parts on a the given circle so you needs to consider each key term.


Diameter – The distance across the circle going through the centre.


Tangent –  A straight line that touches the circle at a single point only.


Circumference – The distance once around the circle.

Parts of a Circle Example 6 step 2 1

Common misconceptions

  • Confusing the Radius/Diameter

The radius is from the centre of the circle to the circumference whilst the diameter goes across the whole circle whilst going through the origin.

  • Confusing the Segment/Sector

A segment is made from a chord whilst a sector will have lines (radii) coming from the origin.

HINT: Some students like to consider a sector like a slice of pizza.

  • Confusing the Chord/Diameter

A chord will not go through the origin of the circle whilst the diameter will.

  • Confusing the Tangent/Secant

A tangent only touches the circumference at a single point, it does not cross the line. A secant will cross the circumference twice.

Practice parts of a circle questions

1. If a circle has an ‘o’ noted on it. It normally notes the

Circle is an o shape

GCSE Quiz False

Middle of the circle (origin)

GCSE Quiz True

Name of the circle is O

GCSE Quiz False

A circle inside a circle

GCSE Quiz False

The ‘o’ refers to the centre of the circle which is called the origin of the circle

2. Which will be the longest in length of any circle

Radius

GCSE Quiz False

Diameter

GCSE Quiz False

Chord

GCSE Quiz False

Circumference

GCSE Quiz True

The circumference is the distance around the edge of the circle, this will always be longer

3. Half a circle is called:

A Semi Circle

GCSE Quiz True

A Half circle

GCSE Quiz False

A double quadrant

GCSE Quiz False

A 180 degree circle

GCSE Quiz False

4. A line that touches the circumference of a circle at one point is called a:

A secant

GCSE Quiz False

A segment

GCSE Quiz False

A Tangent

GCSE Quiz True

An Arc

GCSE Quiz False

5. Which of the following statements is true?

The radius is twice the length of the diameter

GCSE Quiz False

The diameter is twice the length of the radius

GCSE Quiz True

The radius is half the length of the circumference

GCSE Quiz False

The diameter is half the length of the circumference

GCSE Quiz False

The distance from the centre of the circle to the circumference is called the radius. The distance across the circle passing through the centre is called diameter. This means that the diameter is twice as long as the radius.

 

6. A sector is:

Part of a circle’s circumference

GCSE Quiz False

Part of a circle’s area

GCSE Quiz True

A line that goes through a circle

GCSE Quiz False

The middle of a circle

GCSE Quiz False

A sector consists of the area created by an arc and two radii

 

Parts of a circle GCSE questions

1. Name the part of the circle shown in the diagram below:

 

Parts of a Circle GCSE questions 1 1

 

(1 mark)

Show answer

Chord

(1)

2. Name the part of the circle shown in the diagram below:

 

Parts of a Circle GCSE questions 2 1

 

(1 mark)

Show answer

Tangent

(1)

3. Name the part of the circle shown in the diagram below:

 

Parts of a Circle GCSE questions 3 1

 

(1 mark)

Show answer

Sector

(1)

4. Name the part of the circle shown in the diagram below:

 

Parts of a Circle GCSE questions 4 1

 

(1 mark)

Show answer

Diameter

(1)

5. Name the part of the circle shown in the diagram below:

 

Parts of a Circle GCSE questions 5 1

 

(1 mark)

Show answer

Radius

(1)

6. Name the part of the circle shown in the diagram below:

 

‘A line that goes across the circle but does not go through the origin’

 

(1 mark)

Show answer

Chord

(1)

7. Molly says ‘A chord is the same as a radius but shorter’. Is Molly correct? Explain your answer

 

(1 mark)

Show answer

No, the radius goes from the origin to the circumference. A chord does not touch the origin of the circle

(1)

Learning checklist

You have now learned how to:

  • Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference (F)
  • Identify and apply circle definitions and properties, including tangent, arc, sector and segment (F+)

The next lessons are

  • Calculate the area of a circle (F)
  • Calculate the circumference of a circle (F)
  • Find the area of a sector (F)
  • Find the perimeter of a sector (F)
  • Find the length of an arc (F)
  • Find the area of segment (H)
  • Find the perimeter of a segment (H)
  • Write the equation of a circle (H)
  • Identify and use circle theorems (H)

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