Then ,
and form the sides of a triangle. The triangle is
degenerate if and only if the similitude center
of
and
lies on the circumcircle of these triangles.
Bottema, O. Verscheidenheden. Groningen, Netherlands: Wolters-Noordhoff/NVvW, pp. 134-137, 1977.Pinkerton, P. "Note
on Mr. Tweedie's Theorem in Geometry." Edinburgh Math. Soc. Proc.22,
27, 1904.Tweedie, C. "Inequality Theorem Regarding the Lines Joining
Corresponding Vertices of Two Equilateral, or Directly Similar, Triangles."
Edinburgh Math. Soc. Proc.22, 22-26, 1904.