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,

enter image description here

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?
  • 1
    $\begingroup$ 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

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.