What are circle theorems?

Circle theorems are an essential part of every Mathematics GCSE and IGCSE syllabus. Students should have a good understanding of each of the seven circle theorems, as well as how to apply them to examination questions. While the IGCSE and GCSE syllabuses are certainly packed, circle theorems make up a decent portion of the geometry section of the examination.

Circle theorems are used to show the relationship between angles within the geometry of a circle. Mathematicians can use these theorems along with prior knowledge of other angle properties to calculate missing angles, without the use of a protractor. These theorems can be used to solve a variety of mathematical problems, and can incorporate the use of Pythagoras’ theorem and trigonometry.

Key terms within circle theorems

Many GCSE and IGCSE Maths students find circle theorems confusing due to the variety of specific terminology that is required in responses. This terminology will help learners identify the correct theorem to apply to a given question.

First, GCSE and IGCSE candidates must be able to recognise the chords within a problem, these are straight lines with endpoints on the circumference. The diameter, the line that bisects a circle, is an example of a chord.

Usually, students will be asked to calculate the angle of two chords within a circle (in this case, we would say that the angle subtends between the chords), and the methods for these calculations are expressed in the circle theorems.

A step-by-step guide

A typical IGCSE/GCSE problem relating to circle theorems will be to find the size of the angles within a circle. Let us look at the problem below as an example:

At first you are only given one angle within the triangle. However, we know that angle ‘a’ will be 90° due to the application of a circle theorem—the angle at the circumference in a semicircle is always a right angle. This means that angle ‘a’ must be 90°. Now that we have 2 angles, we can calculate the missing angle ‘b’.

Thanks to the application of another circle theorem, we also know that all interior angles in a triangle add up to 180°.

This makes our calculation for angle ‘b’ in the problem rather straightforward.

60° + 90° = 150°

180° - 150° = 30°

Therefore, b = 30°

Asking for help

Like with any formula, the best way to memorise circle theorems is through combining the use of flashcards with frequent practice of past exam questions. This way, students become more familiar and confident with both what the theorems are, and how to apply them in the IGCSE and GCSE exams.

Of course, some learners may require further practice and guidance, in which case BartyED’s team of expert Mathematics tutors are ready to support any student through their GCSE and IGCSEs. If you or your child could benefit from bespoke IGCSE or GCSE Mathematics lessons delivered by expert tutors then reach out to us today by phone (+852 2882 1017) or email (enquiries@bartyed.com).