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K852

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X(3), X(4), X(1657)

infinite points of K003

points of pK(X6, X1657) on (O)

foci of the inconic with center X(20)

other points below

K852 = spK(X3, X20) is a stelloid with radial center X(376) and asymptotes parallel to those of K003. See CL055 and also Table 54.

Its isogonal transform is spK(X1657, X20), a CircumNormal cubic.

K852 passes through the foci of the inconic with center X(20). The axes of this conic are the parallels at X(20) to the asymptotes of the Kiepert hyperbola. The third points P1, P2 of K852 on these axes also lie on the line X(4)X(69).

K852 meets BC at A' on the parallel at X(1657) to the line OA, B' and C' likewise.

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K852 belongs to the pencils generated by :

K004 and K187. See Table 54, line Q = X20 in the table. All these cubics pass through the foci of the inconic with center X(20). See also K855.

K003 and the union of the line at infinity and the Jerabek hyperbola. See Table 54, column P = X3 in the table. All these cubics pass through X(4) and the infinite points of K003. The tangent at X(4) (when defined i.e. when the cubic is not K028) passes through X(51) for every cubic.