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X(2), X(4), X(3413), X(3414), X(5000), X(5001)

points of pK(X6, X193) on the circumcircle

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+a^2 b^2+3 b^4+a^2 c^2-6 b^2 c^2+3 c^4 : : , with SEARCH = 4.25747456165957.

The tangents at A, B, C to Q117 are the symmedians.