Dado un triángulo ABC y un punto P, sea DEF el triángulo circunceviano de P. Denotamos por A'B'C' el triángulo determinado por las rectas de Simson-Wallace de los puntos D, E y F. 

El Lugar geométrico de los puntos P tales que los triángulos semejantes (no simétricos) DEF y A'B'C' sean perspectivos es una séxtica con puntos dobles en los vértices de ABC:



2*a^6*b^2*c^4*x^4*y^2 + 2*a^4*b^4*c^4*x^4*y^2 - 10*a^2*b^6*c^4*x^4*y^2 + 
 6*b^8*c^4*x^4*y^2 + 2*a^4*b^2*c^6*x^4*y^2 + 4*a^2*b^4*c^6*x^4*y^2 - 
 6*b^6*c^6*x^4*y^2 - 10*a^2*b^2*c^8*x^4*y^2 - 6*b^4*c^8*x^4*y^2 + 
 6*b^2*c^10*x^4*y^2 + 2*a^8*c^4*x^3*y^3 + 8*a^6*b^2*c^4*x^3*y^3 - 
 20*a^4*b^4*c^4*x^3*y^3 + 8*a^2*b^6*c^4*x^3*y^3 + 2*b^8*c^4*x^3*y^3 - 
 2*a^6*c^6*x^3*y^3 + 2*a^4*b^2*c^6*x^3*y^3 + 2*a^2*b^4*c^6*x^3*y^3 - 
 2*b^6*c^6*x^3*y^3 - 6*a^4*c^8*x^3*y^3 - 20*a^2*b^2*c^8*x^3*y^3 - 
 6*b^4*c^8*x^3*y^3 + 10*a^2*c^10*x^3*y^3 + 10*b^2*c^10*x^3*y^3 - 
 4*c^12*x^3*y^3 + 6*a^8*c^4*x^2*y^4 - 10*a^6*b^2*c^4*x^2*y^4 + 
 2*a^4*b^4*c^4*x^2*y^4 + 2*a^2*b^6*c^4*x^2*y^4 - 6*a^6*c^6*x^2*y^4 + 
 4*a^4*b^2*c^6*x^2*y^4 + 2*a^2*b^4*c^6*x^2*y^4 - 6*a^4*c^8*x^2*y^4 - 
 10*a^2*b^2*c^8*x^2*y^4 + 6*a^2*c^10*x^2*y^4 - a^8*b^2*c^2*x^4*y*z + 
 6*a^4*b^6*c^2*x^4*y*z - 8*a^2*b^8*c^2*x^4*y*z + 3*b^10*c^2*x^4*y*z - 
 4*a^4*b^4*c^4*x^4*y*z - 8*a^2*b^6*c^4*x^4*y*z + 12*b^8*c^4*x^4*y*z + 
 6*a^4*b^2*c^6*x^4*y*z - 8*a^2*b^4*c^6*x^4*y*z - 30*b^6*c^6*x^4*y*z - 
 8*a^2*b^2*c^8*x^4*y*z + 12*b^4*c^8*x^4*y*z + 3*b^2*c^10*x^4*y*z - 
 a^10*c^2*x^3*y^2*z + 6*a^6*b^4*c^2*x^3*y^2*z - 8*a^4*b^6*c^2*x^3*y^2*z + 
 3*a^2*b^8*c^2*x^3*y^2*z + 2*a^8*c^4*x^3*y^2*z + 2*a^6*b^2*c^4*x^3*y^2*z - 
 22*a^4*b^4*c^4*x^3*y^2*z + 14*a^2*b^6*c^4*x^3*y^2*z + 4*b^8*c^4*x^3*y^2*z + 
 2*a^6*c^6*x^3*y^2*z - 2*a^4*b^2*c^6*x^3*y^2*z - 22*a^2*b^4*c^6*x^3*y^2*z - 
 10*b^6*c^6*x^3*y^2*z - 8*a^4*c^8*x^3*y^2*z - 2*a^2*b^2*c^8*x^3*y^2*z + 
 6*b^4*c^8*x^3*y^2*z + 7*a^2*c^10*x^3*y^2*z + 2*b^2*c^10*x^3*y^2*z - 
 2*c^12*x^3*y^2*z + 3*a^8*b^2*c^2*x^2*y^3*z - 8*a^6*b^4*c^2*x^2*y^3*z + 
 6*a^4*b^6*c^2*x^2*y^3*z - b^10*c^2*x^2*y^3*z + 4*a^8*c^4*x^2*y^3*z + 
 14*a^6*b^2*c^4*x^2*y^3*z - 22*a^4*b^4*c^4*x^2*y^3*z + 
 2*a^2*b^6*c^4*x^2*y^3*z + 2*b^8*c^4*x^2*y^3*z - 10*a^6*c^6*x^2*y^3*z - 
 22*a^4*b^2*c^6*x^2*y^3*z - 2*a^2*b^4*c^6*x^2*y^3*z + 2*b^6*c^6*x^2*y^3*z + 
 6*a^4*c^8*x^2*y^3*z - 2*a^2*b^2*c^8*x^2*y^3*z - 8*b^4*c^8*x^2*y^3*z + 
 2*a^2*c^10*x^2*y^3*z + 7*b^2*c^10*x^2*y^3*z - 2*c^12*x^2*y^3*z + 
 3*a^10*c^2*x*y^4*z - 8*a^8*b^2*c^2*x*y^4*z + 6*a^6*b^4*c^2*x*y^4*z - 
 a^2*b^8*c^2*x*y^4*z + 12*a^8*c^4*x*y^4*z - 8*a^6*b^2*c^4*x*y^4*z - 
 4*a^4*b^4*c^4*x*y^4*z - 30*a^6*c^6*x*y^4*z - 8*a^4*b^2*c^6*x*y^4*z + 
 6*a^2*b^4*c^6*x*y^4*z + 12*a^4*c^8*x*y^4*z - 8*a^2*b^2*c^8*x*y^4*z + 
 3*a^2*c^10*x*y^4*z + 2*a^6*b^4*c^2*x^4*z^2 + 2*a^4*b^6*c^2*x^4*z^2 - 
 10*a^2*b^8*c^2*x^4*z^2 + 6*b^10*c^2*x^4*z^2 + 2*a^4*b^4*c^4*x^4*z^2 + 
 4*a^2*b^6*c^4*x^4*z^2 - 6*b^8*c^4*x^4*z^2 - 10*a^2*b^4*c^6*x^4*z^2 - 
 6*b^6*c^6*x^4*z^2 + 6*b^4*c^8*x^4*z^2 - a^10*b^2*x^3*y*z^2 + 
 2*a^8*b^4*x^3*y*z^2 + 2*a^6*b^6*x^3*y*z^2 - 8*a^4*b^8*x^3*y*z^2 + 
 7*a^2*b^10*x^3*y*z^2 - 2*b^12*x^3*y*z^2 + 2*a^6*b^4*c^2*x^3*y*z^2 - 
 2*a^4*b^6*c^2*x^3*y*z^2 - 2*a^2*b^8*c^2*x^3*y*z^2 + 2*b^10*c^2*x^3*y*z^2 + 
 6*a^6*b^2*c^4*x^3*y*z^2 - 22*a^4*b^4*c^4*x^3*y*z^2 - 
 22*a^2*b^6*c^4*x^3*y*z^2 + 6*b^8*c^4*x^3*y*z^2 - 8*a^4*b^2*c^6*x^3*y*z^2 + 
 14*a^2*b^4*c^6*x^3*y*z^2 - 10*b^6*c^6*x^3*y*z^2 + 3*a^2*b^2*c^8*x^3*y*z^2 + 
 4*b^4*c^8*x^3*y*z^2 - a^12*x^2*y^2*z^2 + 9*a^8*b^4*x^2*y^2*z^2 - 
 16*a^6*b^6*x^2*y^2*z^2 + 9*a^4*b^8*x^2*y^2*z^2 - b^12*x^2*y^2*z^2 - 
 4*a^8*b^2*c^2*x^2*y^2*z^2 + 4*a^6*b^4*c^2*x^2*y^2*z^2 + 
 4*a^4*b^6*c^2*x^2*y^2*z^2 - 4*a^2*b^8*c^2*x^2*y^2*z^2 + 
 9*a^8*c^4*x^2*y^2*z^2 + 4*a^6*b^2*c^4*x^2*y^2*z^2 - 
 90*a^4*b^4*c^4*x^2*y^2*z^2 + 4*a^2*b^6*c^4*x^2*y^2*z^2 + 
 9*b^8*c^4*x^2*y^2*z^2 - 16*a^6*c^6*x^2*y^2*z^2 + 4*a^4*b^2*c^6*x^2*y^2*z^2 + 
 4*a^2*b^4*c^6*x^2*y^2*z^2 - 16*b^6*c^6*x^2*y^2*z^2 + 9*a^4*c^8*x^2*y^2*z^2 - 
 4*a^2*b^2*c^8*x^2*y^2*z^2 + 9*b^4*c^8*x^2*y^2*z^2 - c^12*x^2*y^2*z^2 - 
 2*a^12*x*y^3*z^2 + 7*a^10*b^2*x*y^3*z^2 - 8*a^8*b^4*x*y^3*z^2 + 
 2*a^6*b^6*x*y^3*z^2 + 2*a^4*b^8*x*y^3*z^2 - a^2*b^10*x*y^3*z^2 + 
 2*a^10*c^2*x*y^3*z^2 - 2*a^8*b^2*c^2*x*y^3*z^2 - 2*a^6*b^4*c^2*x*y^3*z^2 + 
 2*a^4*b^6*c^2*x*y^3*z^2 + 6*a^8*c^4*x*y^3*z^2 - 22*a^6*b^2*c^4*x*y^3*z^2 - 
 22*a^4*b^4*c^4*x*y^3*z^2 + 6*a^2*b^6*c^4*x*y^3*z^2 - 10*a^6*c^6*x*y^3*z^2 + 
 14*a^4*b^2*c^6*x*y^3*z^2 - 8*a^2*b^4*c^6*x*y^3*z^2 + 4*a^4*c^8*x*y^3*z^2 + 
 3*a^2*b^2*c^8*x*y^3*z^2 + 6*a^10*c^2*y^4*z^2 - 10*a^8*b^2*c^2*y^4*z^2 + 
 2*a^6*b^4*c^2*y^4*z^2 + 2*a^4*b^6*c^2*y^4*z^2 - 6*a^8*c^4*y^4*z^2 + 
 4*a^6*b^2*c^4*y^4*z^2 + 2*a^4*b^4*c^4*y^4*z^2 - 6*a^6*c^6*y^4*z^2 - 
 10*a^4*b^2*c^6*y^4*z^2 + 6*a^4*c^8*y^4*z^2 + 2*a^8*b^4*x^3*z^3 - 
 2*a^6*b^6*x^3*z^3 - 6*a^4*b^8*x^3*z^3 + 10*a^2*b^10*x^3*z^3 - 
 4*b^12*x^3*z^3 + 8*a^6*b^4*c^2*x^3*z^3 + 2*a^4*b^6*c^2*x^3*z^3 - 
 20*a^2*b^8*c^2*x^3*z^3 + 10*b^10*c^2*x^3*z^3 - 20*a^4*b^4*c^4*x^3*z^3 + 
 2*a^2*b^6*c^4*x^3*z^3 - 6*b^8*c^4*x^3*z^3 + 8*a^2*b^4*c^6*x^3*z^3 - 
 2*b^6*c^6*x^3*z^3 + 2*b^4*c^8*x^3*z^3 + 4*a^8*b^4*x^2*y*z^3 - 
 10*a^6*b^6*x^2*y*z^3 + 6*a^4*b^8*x^2*y*z^3 + 2*a^2*b^10*x^2*y*z^3 - 
 2*b^12*x^2*y*z^3 + 3*a^8*b^2*c^2*x^2*y*z^3 + 14*a^6*b^4*c^2*x^2*y*z^3 - 
 22*a^4*b^6*c^2*x^2*y*z^3 - 2*a^2*b^8*c^2*x^2*y*z^3 + 7*b^10*c^2*x^2*y*z^3 - 
 8*a^6*b^2*c^4*x^2*y*z^3 - 22*a^4*b^4*c^4*x^2*y*z^3 - 
 2*a^2*b^6*c^4*x^2*y*z^3 - 8*b^8*c^4*x^2*y*z^3 + 6*a^4*b^2*c^6*x^2*y*z^3 + 
 2*a^2*b^4*c^6*x^2*y*z^3 + 2*b^6*c^6*x^2*y*z^3 + 2*b^4*c^8*x^2*y*z^3 - 
 b^2*c^10*x^2*y*z^3 - 2*a^12*x*y^2*z^3 + 2*a^10*b^2*x*y^2*z^3 + 
 6*a^8*b^4*x*y^2*z^3 - 10*a^6*b^6*x*y^2*z^3 + 4*a^4*b^8*x*y^2*z^3 + 
 7*a^10*c^2*x*y^2*z^3 - 2*a^8*b^2*c^2*x*y^2*z^3 - 22*a^6*b^4*c^2*x*y^2*z^3 + 
 14*a^4*b^6*c^2*x*y^2*z^3 + 3*a^2*b^8*c^2*x*y^2*z^3 - 8*a^8*c^4*x*y^2*z^3 - 
 2*a^6*b^2*c^4*x*y^2*z^3 - 22*a^4*b^4*c^4*x*y^2*z^3 - 
 8*a^2*b^6*c^4*x*y^2*z^3 + 2*a^6*c^6*x*y^2*z^3 + 2*a^4*b^2*c^6*x*y^2*z^3 + 
 6*a^2*b^4*c^6*x*y^2*z^3 + 2*a^4*c^8*x*y^2*z^3 - a^2*c^10*x*y^2*z^3 - 
 4*a^12*y^3*z^3 + 10*a^10*b^2*y^3*z^3 - 6*a^8*b^4*y^3*z^3 - 
 2*a^6*b^6*y^3*z^3 + 2*a^4*b^8*y^3*z^3 + 10*a^10*c^2*y^3*z^3 - 
 20*a^8*b^2*c^2*y^3*z^3 + 2*a^6*b^4*c^2*y^3*z^3 + 8*a^4*b^6*c^2*y^3*z^3 - 
 6*a^8*c^4*y^3*z^3 + 2*a^6*b^2*c^4*y^3*z^3 - 20*a^4*b^4*c^4*y^3*z^3 - 
 2*a^6*c^6*y^3*z^3 + 8*a^4*b^2*c^6*y^3*z^3 + 2*a^4*c^8*y^3*z^3 + 
 6*a^8*b^4*x^2*z^4 - 6*a^6*b^6*x^2*z^4 - 6*a^4*b^8*x^2*z^4 + 
 6*a^2*b^10*x^2*z^4 - 10*a^6*b^4*c^2*x^2*z^4 + 4*a^4*b^6*c^2*x^2*z^4 - 
 10*a^2*b^8*c^2*x^2*z^4 + 2*a^4*b^4*c^4*x^2*z^4 + 2*a^2*b^6*c^4*x^2*z^4 + 
 2*a^2*b^4*c^6*x^2*z^4 + 3*a^10*b^2*x*y*z^4 + 12*a^8*b^4*x*y*z^4 - 
 30*a^6*b^6*x*y*z^4 + 12*a^4*b^8*x*y*z^4 + 3*a^2*b^10*x*y*z^4 - 
 8*a^8*b^2*c^2*x*y*z^4 - 8*a^6*b^4*c^2*x*y*z^4 - 8*a^4*b^6*c^2*x*y*z^4 - 
 8*a^2*b^8*c^2*x*y*z^4 + 6*a^6*b^2*c^4*x*y*z^4 - 4*a^4*b^4*c^4*x*y*z^4 + 
 6*a^2*b^6*c^4*x*y*z^4 - a^2*b^2*c^8*x*y*z^4 + 6*a^10*b^2*y^2*z^4 - 
 6*a^8*b^4*y^2*z^4 - 6*a^6*b^6*y^2*z^4 + 6*a^4*b^8*y^2*z^4 - 
 10*a^8*b^2*c^2*y^2*z^4 + 4*a^6*b^4*c^2*y^2*z^4 - 10*a^4*b^6*c^2*y^2*z^4 + 
 2*a^6*b^2*c^4*y^2*z^4 + 2*a^4*b^4*c^4*y^2*z^4 + 2*a^4*b^2*c^6*y^2*z^4 =0