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X(3233), X(3234) foci of the Kiepert and Yff parabolas

vertices of the cevian triangle of X(69)

Q078 is the locus of vertices of inscribed parabolas.

Q078 is a bicircular quartic that meets the circumcircle at the same points as nK0(X6, R) with R = 3a^2b^2c^2 + a^2(b^2+c^2)(a^2+b^2+c^2) : : , a point on the line X(2), X(39), X(76), etc.