Circle theorem proof

How do you prove that:

Inscribed angles subtended by the same arc of a circle are equal?

Diagram: http://i61.servimg.com/u/f61/13/61/85/57/circle12.jpg

Sorry, I've been away for the past five days and just got back yesterday.

Anyway, calling the intersection point (the one near the center of the circle) point E, then I think there is a theorem that says CE*AE=DE*BE, or CE/DE=BE/AE, meaning that CD is proportional to DE and BE is proportional to AE, and since angle DEA is congruent to angle CBE (I think these are called "vertical angles" - my sister is taking geometry), then triangle AED is similar to triangle BEC, and its corresponding angles, including angle a and angle b, are congruent.

I actually took a look at this yesterday too, but for some reason I was thinking that CE/AE=DE/BE, which didn't make sense (then I realized today that CE*AE=DE*BE would make sense, after looking at the picture again).

very nice, thank you