Did you know that mathematicians have been studying circles for centuries, pretty much since the invention of the wheel?

Who would have thought the humble wheel could keep us working all these years later.

Every maths teacher you have known will have taught you things about a circle.

Are you able to follow what your teacher says all of the time? Or do they go off on a tangent? Do you go off on a tangent?

Going off at a tangent can help us with circle theorems. It teaches us some properties (facts).

Lets investigate

Also the radii from the centre are of equal length.

Can you see that a quadrilateral is formed?

These facts help us to solve problems.

Example 1

Above you can see where the tangents meet the edge of the circle. This forms an isosceles triangle. (two side lengths the same and the base angles the same)

Angle x can now be worked out.

180 - 80 = 100° 100 ÷ 2 = 50°. Therefore angle x = 50°

Example 2

This is one of the circle theorems that you may be given to help find a side length.

To do this you would use Pythagoras' Theorem, because right angles are formed.

To find the length OA you would apply this theorem.

12 cm² + 5 cm² = 169 cm² √169 = 13 cm

Ready to chase this one down?

Note: Circle theorems also need you to recall other properties from other basic shapes. (hint quadrilaterals, isosceles triangles)