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X(523), X(690), X(879), X(882), X(5466), X(14295), X(16230)

isogonal conjugate of X(4230)

A', B', C' : traces of the trilinear polar of X(115)

Geometric properties :

K979 is the isogonal transform of K147 and the isotomic transform of K052. See below.

It has three real asymptotes :

• one is the line X(2)X(690),

• two are perpendicular to the Euler line and symmetric about G.

The pivotal conic (C) is inscribed in the anticevian triangle of X(523) and it is tangent to the parallel asymptotes. (C) also contains the root X(115).

K979 is the barycentric products X115 x K052, X338 x K147, X523 x K185, X1577 x K221, X850 x K222, X14618 x K908, X525 x K954, X76 x K978 hence we have a family of nine cubics all connected between themselves under some barycentric multiplication and/or some isoconjugation.

The diagram below shows these cubics and some of the transformations mentioned above.