• > I found a new point with a nice property here.
    http://artofproblemsolving.com/community/c6h1483832p8674661

    > Questions:

    > 1. What are the barycentric coordinates of this point?
     
    a^2 (a^8-2 a^6 b^2+2 a^2 b^6-b^8-2 a^6 c^2+3 a^4 b^2 c^2-b^6 c^2+4 b^4 c^4+2 a^2 c^6-b^2 c^6-c^8) : :
    > 2. Is this listed in ETC?
     
    no (under X13607), SEARCH = -55.5256979531121
    > 3. Are there more beautiful properties of this point?

    X(3) can be replaced by any point on the line X(3), X(69), X(332), etc, and you have the same property.
     
    Best regards
     
    Bernard Gibert