Fourth circle theorem

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

Angles in a Cyclic Quadrilateral

Fourth circle theorem:

What's the connection between pairs of opposite angles (α and γ or β and δ)? *

You can use the cursor to move any of points C, D, E or F around the circumference, and hence alter some of the angles.
You can also move point A or B to change the size of the circle.

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

* Hint: Add the pair of angles!
If you need them, the seven circle theorems here

Tim Devereux, Created with GeoGebra