Consider the Vecten configuration of triangle ABC. Show that triangles ABC and LMN are perspective, their perspectivity center (P : Vecten point of the triangle ABC) lying in the line joining their circumcenters J and Q respectively. Show also that the ratio k = |PJ|/|PQ| is always greater or equal to sqrt(3)+1, the equality being valid only in the case ABC is equilateral. Look at Vecten.html for the definitions. The triangles LMN and OST are anti-similar with respect to P, their similarity ratio being k.

Look at Vecten_Equilateral.html for the case of the Vecten configuration, constructed on an equilateral triangle.