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MathematicsSS2 – SS3 / IGCSE5 sessions

Master circle theorems in one week

Seven theorems, one drawing each. The order matters more than the memorising.

Circle theorems are the clearest case of a topic that is impossible to memorise and easy to see. Learn them in construction order and each one implies the next.

Session 1: Angle at the centre

Ask the tutor to draw one arc and both angles, then to drag the circumference point while the angles update. The invariance is the whole lesson.

Session 2: Angles in the same segment

This is the previous theorem with the centre removed. Ask for it in that framing and you have one fact, not two.

Sessions 3–5: The rest, then mixed problems

  • Cyclic quadrilateral, opposite angles
  • Tangent–radius perpendicularity
  • Alternate segment theorem
  • Equal tangents from an external point
  • Then: past-paper questions that need two theorems at once

Guides are written by the Santi learning team and updated each term as exam boards change. Spotted something out of date? Tell us.

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