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K1148

(b + c - 2a) (y - z) y z = 0

X(2), X(369), X(519), X(903), X(4370), X(7026), X(7043), X(9460)

midpoints A', B', C' of ABC

infinite points of the Steiner ellipses

Geometric properties :

K1148 is an example of pK passing through X(369). See also K311 and Table 42, for further details and other cubics.

The polar conic (C) of X(519) is the circum-hyperbola with perspector X(900) and center X(35092). It follows that the tangents to K1148 at A, B, C, G are parallel to the line passing through X(1), X(2) and parallel to the real asymptote which meets K1148 again at X(4370), a point on the Steiner inellipse (S'). The two imaginary asymptotes meet at X(1086), also on (S').

The polar conic (C') of X(4370) is the bicevian hyperbola C(X2, X17780). It is the complement of the circum-hyperbola with perspector X(6544) and center X(1647).