What Kimberling point is this? Any chance it is the new one?
I am fairly new to this and have some amateurish understanding of the basic concepts (Brocard points, conjugations, trilinear coordinates, etc) and a bit of geometric imagination. Frankly I don't quite get it is there some way to identify coordinates of the given point with the help of computer, or it should always be done manually (that task is obviously far beyond my current competence)
Specifically, I found the following construction:
The point D is the circumcenter of the triangle ABC. Then E,F,G are the circumcenters of the triangles ABD, BDC, ADC accordingly. Continuations of the sides of the triangles ABC and EFG always meet in 3 points J,H,I that apparently always lie on a common line. In such case (according to the converse to Desargues' theorem) lines BG, AF, CE always intersect at point K.
K must be a well known triangle center. I suspect it is probably already included in the Kimberling database. Could someone please give a hint on how exactly to look for whether this point is already well-known or the new one...
Probably not going to annoy you with the further requests!