This video is all about tangent proof – where a line touches a circle, and is aimed at GCSE maths grade 8. The whole idea is that it can be treated in a similar way to solving quadratic simultaneous equations, by substitution, but in this case there is only a single point.

Prove algebraically that the straight line with the equation x – 2y = 10 is a tangent to the circle with equation x² + y² = 20

Here’s a link to the question: QT Proof of tangent

and here’s the answer paper: QT Proof of tangent ANSWER – apologies for the fairly basic pdf – it might be better to watch the video 🙂

Tangent proof questions are usually non calculator, and generally 4 – 5 marks. The questions appear in all the main GCSE exam boards – Edexcel, AQA, OCR and Educas. They are popular and, once you have the basic principles, fairly similar.

Please do stop the video, try the question and compare your solution.

**Top Tips!**

- It’s useful to draw the question first to try to understand what they are asking 🙂
- Tangent means that the straight line touches the circle once, at the circumference
- There will be only one value of x and y for both equations
- Simultaneous equations, with two solutions, are where the line passes through the circle

If you would like to find out more try these:

Solving simultaneous equations by substitution

Solving a simultaneous quadratic and linear equation

Please do leave a comment below if you are not sure. Alternately you can view my YouTube channel and leave a comment there – I’ll always try to respond as quickly as possible.

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