Dynamic circle geometry

The dynamic circle geometry files on Geogebratube provide students with the opportunity to interact, explore, predict and confirm results in circle geometry. They will be most valuable when the classroom learning encourages group work and discussion.

It is strongly recommended that the theorems are presented in the given numbered sequence (below) and that no more than five theorems are covered in one session.

Subsequently, students will need to practise recognising the theorems in a wide variety of orientations. Provide plenty of exercises which require missing angles to be found.

Verbal explanations of the reasoning are suitable to begin with. Later, more formally written proofs will become appropriate.


  1. Properties of chords and angles
  2. Lines from the centre
  3. Angles at the centre and circumference
  4. The angle in a semi-circle
  5. Angles in the same segment
  6. Angles of cyclic quadrilaterals
  7. Tests for cyclic quadrilaterals (1)
  8. Tests for cyclic quadrilaterals (2)
  9. Tests for cyclic quadrilaterals (3)
  10. The angle between a tangent and a radius
  11. Tangents from an external point
  12. The angle between a tangent and a chord
  13. Intersecting circles
  14. Intersecting chords
  15. Tangents and secants

Curriculum links

Year 10A: Prove and apply angle and chord properties of circles