The 11 circle geometry rules you need to know

Curriculum check:    ✓ Edexcel      ✓ OCR


  1. A tangent and a radius meet at 90°

  2. Two tangents drawn from the same outside point are always equal in length up until the point where they touch the circle.

3. Any line that cuts through the centre of a chord – no matter where the chord or the line are drawn – will also cut through the centre of the circle.

  1. Any 2 radii form an isosceles triangle – they won’t have the usual little tick marks, you will have to spot this for yourself…practice will make perfect!

5. The angle between 2 chords drawn from 1 point on the circumference is half the size of the angle at the centre:

  1. The angle in a semicircle is 90°:

  1. Angles in the same segment are equal:

  1. Opposite angles in a cyclic quadrilateral add up to 180°:

  1. The angle between a chord and a tangent is always equal to the angle in the opposite segment (“the alternate segment theory”):