Locus is linf+circumcircle + q4-a quartic. Equation of the quartic in terms of xyz: a^2 b^2 c^4 x^3 y + b^4 c^4 x^3 y - b^2 c^6 x^3 y - a^4 c^4 x y^3 -a^2 b^2 c^4 x y^3 + a^2 c^6 x y^3 - a^2 b^4 c^2 x^3 z +b^6 c^2 x^3 z - b^4 c^4 x^3 z - a^6 c^2 y^3 z + a^4 b^2 c^2 y^3 z +a^4 c^4 y^3 z + a^4 b^4 x z^3 - a^2 b^6 x z^3 + a^2 b^4 c^2 x z^3 +a^6 b^2 y z^3 - a^4 b^4 y z^3 - a^4 b^2 c^2 y z^3=0
Isodynamic points X(15) and X(16) also lie on the quartic. But ın these cases such triangles are equilateral and have no Euler lines. (Degenerate case).
Locus is linf+circumcircle + q4-a quartic. Equation of the quartic in terms of xyz: a^2 b^2 c^4 x^3 y + b^4 c^4 x^3 y - b^2 c^6 x^3 y - a^4 c^4 x y^3 -a^2 b^2 c^4 x y^3 + a^2 c^6 x y^3 - a^2 b^4 c^2 x^3 z +b^6 c^2 x^3 z - b^4 c^4 x^3 z - a^6 c^2 y^3 z + a^4 b^2 c^2 y^3 z +a^4 c^4 y^3 z + a^4 b^4 x z^3 - a^2 b^6 x z^3 + a^2 b^4 c^2 x z^3 +a^6 b^2 y z^3 - a^4 b^4 y z^3 - a^4 b^2 c^2 y z^3=0
ReplyDeleteIsodynamic points X(15) and X(16) also lie on the quartic. But ın these cases such triangles are equilateral and have no Euler lines. (Degenerate case).
It's Q002-Euler-Morley quartic.
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