The lines AL, BM and CN, joining the vertices with the centers of the opposite squares, pass all through a point K. This is a particular instance of a more general property:

On the sides of the triangle erect isosceli triangles similar to a given isosceles triangle t'. Then the lines joining each vertex of t with the apex of the opposite isosceles pass through a common point K. All these points K, resulting by changing the shape of t', lie on the [Kiepert Hyperbola]. A rectangular hyperbola passing through the vertices of the triangle, the orthocenter and other remarkable points of the triangle.

The file Vecten.html introduces the subject and discusses the first properties of the Vecten configuration of an arbitrary triangle.

For a further study of the subject look at the file: Vecten3.html .

Produced with EucliDraw© |