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X(2), X(376), X(3413), X(3414), X(5000), X(5001)

points of K002 on the circumcircle, vertices of the Thomson triangle

foci of the Steiner inellipse

The degenerate quartic into K018 and the line at infinity and Q019 generate a pencil of circular quartics which contains the quartics Q115, Q116, Q117, Q118.

All these quartics have the same singular focus namely X(187) and their two real asymptotes meet at X on the line X(543)X(625).

Here X = 2 a^4-5 a^2 b^2+5 b^4-5 a^2 c^2-2 b^2 c^2+5 c^4 : : , with SEARCH = 5.06683522281896.