Thales's theorem

For the theorem sometimes called Thales' theorem and pertaining to similar triangles, see intercept theorem.
Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle.

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements.[1] It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras.

  1. ^ Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements. Vol. 2 (Books 3–9) (2nd ed.). Dover. p. 61. ISBN 0486600890. Originally published by Cambridge University Press. 1st edition 1908, 2nd edition 1926.