# Is my proof of 'inscribed angle theorem' different from the usual one?

The usual proof of inscribed circle theorem uses the fact that the sum of interior angles is equal to exterior angle. I've formulated a little different approach, although the underlying concept is still to use isosceles triangle properties. I want to know whether my proof has anything original or not. The proof is,

A,B and C are thrre vertices of the triagnle and O is the circumcenter. By the property of isosceles triangle we have $\delta = \delta _1, \alpha = \alpha _1$ and $\beta = \beta _2$

Now, $$(\angle A - \alpha)+(\angle C - \beta) = 180 - \angle AOC$$ $$\implies \angle AOC = \left( 180-(\angle A + \angle C) \right) + (\beta + \alpha)$$ $$\implies \angle AOC = \angle B + \angle B = 2 \angle B$$

• So the question is, have I done something original?
• There are more than one way to prove the validity of the said theorem and some are more simpler. – Mick Jul 22 '15 at 13:42
• @Mick Could you give a link to those proofs? – user103816 Jul 22 '15 at 15:22
• Search for "angle at center is twice the angle at circumference". – Mick Jul 22 '15 at 15:28