Circle Theorems

June 27, 2024•2 min read

The question may be like a puzzle that you need to pick away at the get to the actual point.

Circle theorems are definitely something that people seem to struggle with. I think it’s not because they are difficult, but because there is so much to remember.

The question may be like a puzzle that you need to pick away at the get to the actual point.

When you first look at it, think about what you know at a glance.

From here you can start to ask if that will help you.

There are 7 theorems to learn for the GCSE, which in a nutshell are as follows:

1. When a line leaves each end of the diameter and joins at the circumference, the angle where they meet is always 90 degrees.

2. Two radii which have a line across the bottom to form a triangle will create an isosceles triangle (because the radius is always the same distance from the circumference no matter where it is drawn in the circle, meaning that the base angles will always be the same).

3. If you have a 4-sided shape with each corner touching the circumference, the two opposite corners will add to 180 degrees.

4. Where the tangent (a straight line that touches the outside of the circle) touches the radius, it will again be 90 degrees.

5. A line taking off the edge of a circle is called a chord. If you have triangles anywhere in the circle which reach the circumference and use this same chord as their base. The angle at the circumference will always be the same.

6. Alternate angle theorem. This is apparently the hardest one to learn. Imagine a triangle in a circle which has one corner touching the tangent. (Life is so much easier when I can draw these and show you what I mean!) The areas outside the triangle are called segments. The angle that touches the tangent it equal to the angle in the opposite segment at the circumference. If that makes sense, I will be shocked!

7. Finally, an angle at the circumference is always half the size of the angle at the centre.

If none of that makes sense without diagrams/ video, please do say and I will happily create it.

Dawn Strachan

For the past 20+ years I have been a firm believer that learning should be an enjoyable experience. I appreciate that traditionally education has revolved around worksheets, textbooks, listening to teachers. But a grounding in early years and working with children who had a variety of learning styles from I learned that it is an individual activity that is personal to all of us. We don’t all learn in the same way. Our influences, our experiences, our capabilities all influence how we retain information. But through it all, I believe that if we can make it enjoyable and engaging, they will want to participate. With participation comes practice which in turn boosts skill and confidence. With an increase in skill and confidence comes a willingness to have a go. This in turn leads to more practice which leads to a positive spiral of success. The moral, we need to make learning fun, engaging, use a range of techniques.

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