Intersecting Chords Mastery
An interactive lesson on screen. Your child works through worked examples, practises on their own, then tests themselves with questions that get harder as they go.
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About this lesson
By the end of this lesson your child can use the intersecting chords rules to find a missing length when two chords cross inside a circle, when two lines meet outside it, and when one of those lines is a tangent, then solve the algebra and exam questions built on them. These rules are on the Edexcel IGCSE Higher paper but not on GCSE, and they are not on the formula sheet, so a student who has only been taught the GCSE circle theorems will not have seen them.
An extra IGCSE topic, not a full IGCSE course. This is one of 4 lessons covering the topics on the Edexcel IGCSE Higher specification that GCSE does not teach. It is for students who are already working through the GCSE Higher content. The topics IGCSE shares with GCSE, such as algebra, graphs and trigonometry, are in our GCSE Higher lessons. Intersecting chords is on Edexcel IGCSE (4MA1) only, so it is not needed for Cambridge IGCSE.
Topics covered:
- Chords crossing inside a circle, using AP × PB = CP × PD to find a missing part, a whole chord or the radius when one chord is a diameter
- Algebra inside the circle, setting up and solving linear equations and quadratics, by factorising or with the quadratic formula
- Two lines meeting outside the circle, where each side is the outside part times the whole line, including show that questions
- A tangent and a line through the circle, using PT² = PA × PB, with exact surd answers and the unknown in either length
- The hardest exam types, where the rule is one step in a longer question with Pythagoras, the area of a triangle, the cosine rule or the sine rule
Your child works through this lesson on a laptop or computer, which is the screen size it is built for. They click to reveal each line of a worked example, try the practice questions on paper, then click to check their own answer.
How it's structured:
- Each unit is split into 5 tabs, one per question type, with a worked example your child clicks through line by line, then practice questions colour coded easy, medium and hard
- 27 worked examples and 253 practice questions, each with a click-to-reveal answer, plus New Questions and New Examples buttons that deal fresh numbers every time
- A 20 question final mix pulling from every unit, then 6 exam style IGCSE Higher questions with the worked answer revealed one line at a time
Where the rules come from. Each rule has its own page, and the first two have a Why It Works button that shows the similar triangles behind the rule, one step a click. In the Product Lab your child drags the crossing point anywhere inside or outside the circle and turns the two lines, and the two products stay equal every time. A student who has seen why the rule works finds it much easier to remember in the exam.
Use this if:
- Your child is sitting Edexcel IGCSE Maths Higher (4MA1) and has not been taught intersecting chords yet
- Your child is confident with GCSE Higher content and needs the extra IGCSE topics on top
- Your child knows the rule for chords inside the circle but gets stuck when the lines meet outside it or one of them is a tangent
- You want a resource your child can check their own work with, not one more thing on your to-do list
Built by an experienced maths teacher with over 3,000 hours of one-to-one tutoring experience and a Master's in Education.
Better value as a bundle. This lesson is one of 4 in the IGCSE Higher Maths: The Extra Topics Bundle, all 4 for £21.99 instead of £31.96 bought separately.
Format: Interactive digital lesson, link sent by email straight after purchase.
Suitable for: Year 10 and Year 11, IGCSE Higher (Edexcel 4MA1).
Refunds: this is a digital product delivered instantly, so it cannot be returned or refunded once the link has been opened. If you have any trouble getting in, email info@shlc-tutor.co.uk and we will sort it out.
Who this is for
Built for students who want to practise independently, at their own pace, with clear examples and instant feedback rather than a static worksheet.
What's included
Worked examples
See the method explained step by step before trying it yourself.
Guided practice
Work through questions with answers hidden until you're ready to check.
Exam-style questions
Split easy to hard, so your child is always working at the right level.
How it works
Buy the lesson
Complete checkout securely through Shopify.
Get your link by email
Your lesson link lands in your inbox straight after payment.
Work through it on screen
Open the link on a laptop or computer and start straight away.
What parents say
Aadam, the tutor has a lovely mannerism and has made my daughter feel at ease. He explains the question in a way that she understands and is patient with her. She has already seen the results at school from his help and has gone up two GCSE grades in a short period of time.P. Flower · December 2024
Aadam is the best maths tutor I’ve ever had! His online maths lessons are easy to follow, and he always breaks down difficult topics into manageable parts. Thanks to Aadam’s tutoring, I’ve gone up two grades in maths and feel ready for my GCSE exams!L. Anggriani · December 2024
Aadam has been tutoring my son in preparation for his Yr8 exams and my son achieved a very good mark. This was achieved by Aadam working with my son to identify his weaknesses from the very beginning and to strengthen his foundation. Aadam is very calm and has an excellent structure to his classes.K. Lalla · June 2026
Verified 5-star Google reviews of SHLC's tutoring and lessons. Read all 62 reviews
FAQs
How do I access the lesson?
You'll get an email with your lesson link as soon as payment goes through. Click it to open the lesson in any browser, no login and no app to install.
How does the marking work?
There's no typing answers into a box. Your child works it out on paper, then clicks to reveal the correct answer and checks their own work. Full working is shown too, not just the final answer, so mistakes are easy to spot.
What do I need to open it on?
A laptop or a desktop computer. The lesson puts a worked example, a diagram and a question grid on the page at once, so it needs a full size screen with room for your child's own working beside it. It will open on a phone, but everything is too small to work from and we would not recommend it.
Can I use the lesson more than once?
Yes. There's no limit on how many times you open the link, so it's there for revision right up to the exam.
What if I lose the link or don't get the email?
Email info@shlc-tutor.co.uk and we'll resend it straight away.
Ready to start?
Link sent to your email, ready in seconds
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