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X(51), X(6116), X(6117)

Geometric properties :

K957 is the Hessian of the stelloid K049 hence it is a focal cubic with singular focus X(51), the radial center of K049.

It is the focal cubic K048 of the orthic triangle hence it contains the counterparts of the points of K048 in the orthic triangle. For example, X(2), X(15), X(16) on K048 correspond to X(51), X(6116), X(6117) on K957. The remaining points of K048 correspond to unlisted points in ETC.

The polar conic of X(51) is the circle (C) passing through X(51), X(137), X(138) which is the Parry circle of the orthic triangle.

The orthic line (L) passes through X(5), X(53). It is the Brocard axis of the orthic triangle. The real asymptote of K957 is its homothetic under h(X51, 2).

K957 is the locus of contacts of tangents drawn from X(51) to the circles passing through X(6116), X(6117). These circles are orthogonal to the nine points circle.