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Circle Theorems Worksheet

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Help your students prepare for their Maths GCSE with this free circle theorems worksheet  of 44 questions and answers

  • Section 1 of the circle theorems  worksheet contains 36 skills-based circle theorems questions, in 3 groups to support differentiation
  • Section 2 contains 4 applied circle theorems questions with a mix of worded problems and deeper problem solving questions
  • Section 3 contains 4 foundation and higher level GCSE exam style questions 
  • Answers and a mark scheme for all questions are provided
  • Questions follow variation theory with plenty of opportunities for students to work independently at their own level
  • All questions created by fully qualified expert secondary maths teachers
  • Suitable for GCSE, IGCSE and KS4 maths revision for AQA, OCR and Edexcel exam boards

Download your free resource today

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Circle Theorems at a glance

 

Circle theorems are a set of angle properties that apply within circles. We can use the circle theorems to work out missing angles. 

 

To access circle theorems, we need to be confident with the names of the key parts of a circle including the centre of the circle, the diameter of the circle, the radius of the circle, a tangent to the circle, a segment of the circle, a sector of the circle and a chord within the circle.

 

We also need to be confident at labelling angles using three letter notation. For example, angle BCD is the angle created at C when travelling from B to C to D. The centre of a circle is often labelled O, in which case the angle BOD would be the angle at the centre O when travelling from B to O to D.  

 

The circle theorems are:

  • The angle at the centre is twice the angle at the circumference of a circle
  • Angles in the same segment are equal
  • Opposite angles in a cyclic quadrilateral are equal
  • The angle at the circumference of the circle in a semicircle is a right angle
  • The angle between a tangent and a radius is a right angle
  • Two tangents which meet at a point are equal in length
  • The alternate segment theorem
  • A triangle made from two radii is an isosceles triangle

 

Looking forward, students can then progress to additional geometry worksheets, for example, an area of compound shapes worksheet or how to work out perimeter worksheet. 

 

 

For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts. 

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