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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,

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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?
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    $\begingroup$ There are more than one way to prove the validity of the said theorem and some are more simpler. $\endgroup$ – Mick Jul 22 '15 at 13:42
  • $\begingroup$ @Mick Could you give a link to those proofs? $\endgroup$ – user103816 Jul 22 '15 at 15:22
  • $\begingroup$ Search for "angle at center is twice the angle at circumference". $\endgroup$ – Mick Jul 22 '15 at 15:28

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