Circle Geometry: Alternate Segment Theorem!?

Question

For whatever reason I just do not get the alternate segment theorem (like this: http://library.thinkquest.org/C0110248/geometry/circleast.htm) in circle geometry. Can somebody please explain it to me in great detail of how to work out which angle is the alternate one? I don't get it! Thanks very much.

Answer 1

This should help. Murderous Maths ftw!

Basically, the alternate angle is the one that is in the segment and which is also opposite the original chord.