Circle Theorems GCSE revision and worksheets

Circle Theorems also known as Circle Geometry is a GCSE Maths topic which has a bigger role in the new 9-1 course. There are many types of Circle Theorem questions that can come up but they all require you to know the 8 circle geometry rules off by heart, you don't just need to practise spotting them you also need to describe them. As part of Circle Theorem questions, standard geometry rules appear so ensure you are happy with all of these rules as well.

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What you need to know

What you need to know:

In the higher course, there are a handful of circle theorems – notable facts about angles and lengths in circles – that you are expected to both a) know how to prove, and b) know how to use them to prove other facts about angles in circles, and this includes being able to state which circle theorem you are using at each step of your proof. The circle theorems, listed as you would be required to state them as part of your answer to a question, are as follows:

  1. The angle at the centre is twice the angle at the circumference;
  2. The angle at the circumference in a semi-circle is a right-angle;
  3. Angles in the same segment are equal;
  4. Opposite angles in a cycle quadrilateral add up to 180 \degree ;
  5. A tangent to a circle forms a right-angle with the radius (at that point);
  6. The lengths of two tangents from a single point to a circle are equal;
  7. The perpendicular line from the centre to a chord bisects the chord;
  8. The alternate segment theorem.

There are obviously quite a few of these you have to learn (along with how to prove them), so it is important to take the time to feel comfortable with all of the theorems and their associated proofs.

Students often struggle with Circle Theorem descriptions and remembering the rules even when they can spot them in a question they regularly fail to describe the rule in  way that gets them the marks. Whether you are a Maths tutor in Harrogate or you provide Maths tuition in Leeds, the circle theorem questions and resources on this page will be of great use when setting homework and looking for quality revision materials to pass on to your students.

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