Circle Theorems 1 - 2 Theorems

This applet investigates two important theorems about circles, angles in cyclic quadrilaterals and angles in the same segment

UK Years 10-11, Ages 14-16, KS4, Higher GCSE Mathematics - Geometry, Shape and Space

Instructions below    light background   Waldomaths video   Waldomaths video   Waldomaths video   Waldomaths video  See also: Circle Theorems: 2  3  4  Triangles  Circle Parts

[Applet - Circle theorems 1]

You can move the points A, B, C and D by clicking them and dragging them with your mouse.
By doing this you'll see two important rules about angles inside circles being enacted. Look carefully at the size of the angles. Try to work out the rule before you click the button "Show Theorem" at the bottom.

Clicking the box "Show Chords" will draw two chords which may help you with one of the theorems. Try it.
You will flip from one rule to the other as the lines on the diagram cross over each other. Try it.
Enjoy yourself while you practise and learn these two important theorems by name.