in geometry, thales's theorem states that if a, b, and c are distinct points on a circle where the line is a diameter, then the angle ∠abc is a right angle. thales' 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". it is generally attributed to thales of miletus, who is said to have offered an ox (probably to the god apollo) as a sacrifice of thanksgiving for the discovery, but sometimes it is attributed to pythagoras.