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The normal approach to prove Thale's theorem should be induced from the property of central angle being twice of an inscribed angle that subtends the same arc. Since a diameter has central angle of 180 degrees, its corresponding inscribed angle should be half of 180, that is 90 degrees.


No, because if you do it that way, you wouldn't have Thales's Theorem. It would be Thales's Trivial Corollary.

Thales's Theroem is a simpler, easier to prove (as in OP), less powerful statement than the inscribed angle theorem.


Your second sentence denies the first sentence. The proof of the Inscribed angle theorem does not need Thale's Theorem, and it is stronger than Thale's Theorem.




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