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'Subtended Angles' printed from http://nrich.maths.org/
If you are having difficulty with the interactivity, you may find this helpful:
* To create a rubber band for placing on your peg board, click on the colour of band that you would like to use, in the right-hand-side table.
* A new icon will appear on the screen. Drag this rubber band over to a peg on the board. Let go.
* You can now drag the rubber band to different pegs. To create another rubber band, repeat the above.
Join all the points up to the centre and look for isosceles triangles.
You may find this diagram helpful to get you started.
It is useful to note that the blue lines are all radii of the circle, and as such, are all the same length.
You may want to use some algebra to help explain your proof