Kiepert's theorem states that if similarly oriented similar isosceles triangles 
, 
, and 
are constructed on the three sides
of a triangle 
, then the three lines 
, 
, and 
are concurrent.
The point of concurrence depends on the common apex angle of the three erected triangles. As this angle varies, the concurrence point traces the Kiepert hyperbola. In the special case of erected equilateral triangles, the concurrence point is one of the Fermat points.
