The Vecten configuration of triangle DEF results by constructing squares on the sides of the triangle, called [flanks]. Then extending the sides of the flanks opposite to the triangle sides we get a triangle ABC, similar to DEF. AF is symmedian line of ABC, since the distances of point F from the sides AB, AC are at ratio FM/FH = FD/FE = AB/AC, which is characteristic for the symmedian. Further, AF is also symmedian of DEF through F, since by similarity the symmedian of DEF should divide the angle at F as AF divides the angle at A. Thus the two triangles share the same symmedians, and consequently the same symmedian point K, which is the center of similarity of the two triangles.
The figure shows also how to solve the exercise of construction of triangle DEF, inversely from the triangle ABC: Take the symmedian point K of ABC and consider the construction of squares inscribed in the three triangles AKB, BKC, CKA.Look at file Symmedian_0.html for the elementary facts about symmedians.
![[alogo]](alogo.png){kind=small}
Symmedian and Vecten ![[0_0]](Symmedian_Vecten_files/Symmedian_Vecten_0_0_0.png)
![[0_1]](Symmedian_Vecten_files/Symmedian_Vecten_0_0_1.png)
![[0_2]](Symmedian_Vecten_files/Symmedian_Vecten_0_0_2.png)