Circle theorems · IGCSE Mathematics 0580 Simulation

About this lab: Circle theorems

Interactive simulation for Cambridge IGCSE Mathematics 0580 circle theorems: the parts of a circle, the angle in a semicircle, tangent and radius, tangents from an external point, the angle at the centre, angles in the same segment, cyclic quadrilaterals, the alternate segment theorem and chord properties, each with draggable points, live angles and a proof, plus random find-the-angle questions with the reasons to write.

IGCSE Mathematics 0580, topics 4.1, 4.7 and 4.8. Drag points round the circle and watch each theorem hold, see why it is true, then find angles and give the reasons.

Circle theorems is a free, browser-based simulation for Cambridge IGCSE Mathematics 0580 (topic 4 Geometry, sections 4.1 Geometrical terms, 4.7 Circle theorems I, 4.8 Circle theorems II (Extended)). The course is assessed in Paper 1 (Core non-calculator), Paper 2 (Extended non-calculator), Paper 3 (Core calculator), Paper 4 (Extended calculator). Syllabus for examination in 2025-2027. There are 9 tabs, each a self-contained experiment with its own controls and live readings, and nothing to install: it runs on a laptop, tablet or classroom projector.

Syllabus coverage

4.1 Geometrical terms. Lessons: Geometrical terms: shapes, solids and nets.
4.7 Circle theorems I. Lessons: Circle theorems I: semicircles and tangents, Circle theorems II: centre, segments, cyclic quadrilaterals.
4.8 Circle theorems II (Extended). Lessons: Circle theorems II: centre, segments, cyclic quadrilaterals.

Full syllabus map: IGCSE Mathematics 0580 topic 4.

How to use this simulation

1. Parts of a circle.
2. Semicircle.
3. Tangents.
4. Angle at centre.
5. Same segment.
6. Cyclic quad.
7. Alternate segment.
8. Chords.
9. Find the angle.
The buttons at the end of the tab strip give the scene the whole window (Full screen, Hide controls) and, on a dark stage, a projector-friendly palette (Light scene). Many scenes also have drag handles: drag them to change the set-up directly.

All simulation labs · IGCSE Mathematics 0580 · TheLucidSTEM home