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X(2), X(13), X(14), X(618), X(619), X(3413), X(3414), X(14537)

midpoints of ABC

traces of the trilinear polar (L) of X(1989)

points of K278 on (O)

Q193 is the Laplacian of Q192 i.e. the locus of points whose polar conic in Q192 is a rectangular hyperbola.

Note that the Laplacian of Q193 is the Kiepert hyperbola.

Q193 is a circular quartic with two isotropic asymptotes concurring at G and two real asymptotes concurring at X(36523).

Q193 meets (O) at A, B, C (where the tangents are the medians of ABC), at the circular points at infinity and at three other points which lie on K278.

G is a point of inflexion with inflexional tangent passing through X(187).

The polar line of a point M in Q193 passes through G if and only if M lies on K065 which contains X(2, 13, 14, 67, 524, 2770, 5463, 5464, 34319, 34320) and the circular points at infinity. Recall that K065 is the orthopivotal cubic O(X524), a central focal cubic with center G.