Dear Yakub, 1 --> when using P= p:q:r instead of barycentrics of H, everything turns easier (and a generalization --using a nine-points conic-- is obtained as
I also have sent my calculations, with Mathematica and my package baricentricas.nb I have included the proof of the relation GP:PH = (2-1/(cosA cosB cosC))/3
Dear Hyacinthos I send a file in french with conway notations expleting the mode of calculus The name of the file is "New point on Euler Line" Amically Michel