MathsYears 10–11Geometry - Properties of Shapes

Circle theorems

Apply and prove circle theorems including tangent, chord and cyclic quadrilateral properties

What you'll learn

  1. 1

    Imagine a pizza 🍕 with a dot right in the middle — that's the centre of the circle. A line from the centre to the edge is called a radius.

  2. 2

    What is a line from the centre of a circle to the edge called?

  3. 3

    Drag the points to make a triangle with one corner at the centre and two on the edge. Notice the two sides from the centre are equal — it's isosceles!

  4. 4

    Let's prove: The angle at the centre is twice the angle at the edge (when they both see the same arc).

  5. 5

    If the angle at the centre is 120°, what is the angle at the edge (on the same arc)?

  6. 6

    Move point C around the circle — watch the angle at the edge stay half of the centre angle!

  7. 7

    True or false: The angle at the centre is always bigger than the angle at the edge (on the same arc).

Practise Circle theorems with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 14–16. Aligned to the UK National Curriculum.