Circle Theorems
A collection of resources for learning and understanding circle theorems
Presentation in Microsoft PowerPoint format.  The applet beneath was created in GeoGebra, which is a small, free piece of dynamic geometry software that can be downloaded from:

Introduction and proof of circle theorems:

A comprehensive presentation of the major circle facts and theorems, beginning with naming the parts of a circle and ending with geometric proofs of the theorems.  
Circle Theorems
Circle Theorems presentation

Discovering Circle Theorems using GeoGebra

Use GeoGebra (free download or online versions available) to investigate angles within circles.  Use the following pdf documents:
Intro to GeoGebra
Introduction to GeoGebra
Discovering Circle Theorems with GeoGebra
Discovering Circle Theorems
Discovering Circle Theorems with GeoGebra
Blanks for Circle Theorems

Circle Theorems Applet

To dive straight into investigating or demonstrating, use the applet below: move the points around to illustrate the various theorems. Spot the pairs of equal angles, notice which pairs add up to 180 degrees and learn to appreciate why the circle produces such special properties.  
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Food for thought...

Just because the theorems above are the only ones examinable for GCSE Maths doesn't mean they are the only ones.  Try investigating different shapes and see if you can find any more of your own.  Here's an example of a cyclic hexagon to get you started.  
Cyclic Hexagon - Hint: look at alternate angles.