Special triangle center

[S. B. Gray]

Does anyone know the name of the point that minimizes the sum of the
squared reciprocals of distances from P to the sides? (That is,
Minimum[1/dist(P, side a)^2+1/dist(P, side b)^2+1/dist(P, side c)^2].)
Curiously, this point lies on the line connecting the centroid and the
incenter.

[Lee Rudolph]

Well, then, if you can somehow launch successful campaigs to have
the centroid and the incenter renamed (respectively or the reverse)
the "white center" and the "black center", this new center will
inevitably come to be known as the Gray Center.

Lee Rudolph (well, maybe not; I see that I assumed it's on
the line _segment_ connecting them, which is not what you
wrote...hmmm)

[Dan Cass]

Have a look at the following web site:
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
It's Kimberling's Triangle Center page and has thousands
of known triangle centers.
Maybe writing to Kimberling about your center would lead to some kind of answer...