proof of Thales’ theoremLet M be the center of the circle through A, B and C.Then AM=BM=CM and thus the triangles AMC and BMC are isosceles. If ∠BMC=:α then ∠MCB=90∘-α2 and ∠CMA=180∘-α. Therefore ∠ACM=α2 and∠ACB=∠MCB+∠ACM=90∘.QED.