Circle Theorems – easy as pie 😉

Circle theorems questions are often a source of confusion for many GCSE Maths students.

The main reason for this is because the exam questions always combine at least 2 rules -usually more- and trying to visualise and see all of the different triangles, chords and sectors in the circle can become difficult.

So, how do you get good at circle theorems?

Step 1: Learn each rule off by heart.

Step 2: Practice each rule individually with as many questions as you can find. As this will allow you to see all the different kinds of diagrams you are likely to see in the exam.

Step 3: Practice as many exam style questions on circle theorems as possible so that you get used to interpreting the diagram and ‘see’ the separate rules within.

Let’s have a look at some GCSE Maths past paper questions on Circle Theorems:

Question: Circle the line that is a diameter of the circle. [1 mark]

What’s happening here?

First off, it’s a one mark question. That means the maths isn’t complicated and they’ve given you all the info you need.

Which circle theorem talks about diameters and angles in semi circles?

That’s right, rule 3: The angle in a semi circle is a right angle.

So which triangle has a right angle?

If we look at triangle BFE, the 2 given angles add up to 100, meaning angle meaning angle F must be 80 degrees. So that’s not in a semicircle.

Triangle ACD: The given angles add up to 90, which means angle C must be 90. So that’s in a semicircle meaning the line AD must be a diameter.

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