Babylonian mathematicians knew this for special cases before Greek mathematicians proved it.
Thales of Miletus (early 6th century BC) is traditionally credited … See more

For any triangle, and, in particular, any right triangle, there is exactly one circle containing all three vertices of the triangle. (Sketch of proof. The locus of points equidistant from two given points is a straight line that is called the perpendicular bisector of the line … See more

Constructing a tangent to a circle passing through a point
Thales's theorem can be used to construct the See more

• Weisstein, Eric W. "Thales' Theorem". MathWorld.
• Munching on Inscribed Angles
• Thales's theorem explained, with interactive animation
• Demos of Thales's theorem by Michael Schreiber, See more

First proof
The following facts are used: the sum of the angles in a triangle is equal to 180° and the base angles of an isosceles triangle are equal.
Since OA = OB = OC, △OBA and △OBC are isosceles … See more

As stated above, Thales's theorem is a special case of the inscribed angle theorem (the proof of which is quite similar to the first proof of Thales's theorem given above):
Given three points A, B and C on a circle with center O, the … See more

• Synthetic geometry
• Inverse Pythagorean theorem See more