The Thales’ Circle

Thales was born in Milet in the year 624 BC. He is considered as the first philosopher ever and was a famous mathematician of the ancient world. Among other things the following proposition is attributed to Thales: 'Every angle of a triangle in a semicircle is a right angle.' This semicircle is called the Thales' Circle.

Thales' Circle Thales from Milet

The Thales’ Circle is not only a means to create right angled triangles but also to construct a tangent from a certain point touching on a circle because every tangent is rectangular to the radius running through the one and only point of tangency.

You have to construct a tangent from point P touching on the circle k with centre M. Draw the Thales’ Circle with diameter PM. The tangent runs through point P and through the point of intersection S.