First circle theorem

First page
Theorem 1
Theorem 2
Theorem 3
Theorem 4
Theorem 5
Theorem 6
Theorem 7
The Seven Theorems

Angle at centre and angle at circumference

First circle theorem:

What's the connection between the angle at the centre, α, and the angle at the circumference, β?

You can use the cursor to move point C, and hence to alter angle α.
You can also move point D around the circumference.
If you move point B, then angle α and the size of the circle both change.
Notice what happens to angle β as you make these changes.

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

If you need them, the seven circle theorems here

Tim Devereux, Created with GeoGebra