Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Circles & Circle Theorems
Tangents, chords and the five classical circle theorems — the Higher paper's favourite angle-chase territory.
Every lesson here ends the same way: learn it, teach it to an AI pupil who asks the awkward question, then defend it against the thinker with the strongest claim on it — free · no account needed.
2 modules of Pearson Edexcel International GCSE Mathematics (1 Higher Tier), each explained in full — what it is, why it works, when a question is asking for it, the mistakes that cost marks and worked examples — with five graded questions marked on your own device. Completely free.
The modules in Circles & Circle Theorems
Circle Properties & Tangents
Radii, chords and tangents, and the right angles they secretly generate — the foundation the circle theorems build on. The working parts of a circle: radius (centre to edge), chord (edge to edge), tangent (touches at exactly one point), arc, sector, segment.
When a question is asking for it: Any diagram with a tangent → mark the 90° immediately. Learn Circle Properties & Tangents →
Circle Theorems (Higher Tier)
The five classical theorems — centre and circumference, semicircle, same segment, cyclic quadrilateral, alternate segment — and how to chain them. Higher Tier. The five: (1) the angle at the centre is TWICE the angle at the circumference on the same arc; (2) the angle in a semicircle is 90°; (3) angles in the same segment are equal; (4) opposite angles of a cyclic quadrilateral sum to 180°…
When a question is asking for it: Higher-paper angle chases. Learn Circle Theorems →
The mistakes that cost marks in Circles & Circle Theorems
One from each module — the error examiners see most, with the module that puts it right.
- Marking the tangent angle 90° to the CHORD instead of to the radius at the contact point. (Circle Properties & Tangents)
- Halving in the wrong direction: centre = 2 × circumference. Given the centre angle, HALVE it for the circumference. (Circle Theorems)
Where Circles & Circle Theorems sits in the specification
Content area 4 of 4MA1, sub-topic 4.6. Incandio is aligned to the specification and is not published by Pearson; the numbers are given so you can check every module against your own copy.
- 4.6 — Circle properties — circle theorems (Higher)
How Circles & Circle Theorems is mastered on Incandio
Every module above ends the same way: five questions that climb Grade 6 → 9+, then you teach the method back to Ember, an AI pupil who asks the awkward question, and defend it against the mathematician with the strongest claim on it. Exam Ready carries 18 authored exam-style questions across this strand, marked on Incandio.
All of Incandio Mathematics · The 4MA1 specification · Exam Ready