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K794

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X(2), X(110), X(524), X(858), X(5211), X(5978), X(5979), X(10717)

A'B'C' : circumcevian triangle of X(2)

(contributed by Peter Moses, 2016-04-09)

The Kiepert hyperbola (K) of the first Brocard triangle contains the ETC centers X(i) for i = 2, 3, 76, 599, 1352, 2896, 3094, 3413, 3414, 3642, 3643, 3821, 6228, 6229, 7697, 9743. Its Psi transform is the strophoid K794. See the analogous strophoids K509, K795, K796, also K792, K793.

The nodal tangents at G are the axes of the Steiner ellipses. The real asymptote is the line X(111)X(524).

The singular focus F is X(10717) and the intersection X with the real asymptote is unlisted in ETC with SEARCH = 14.8118767406537.

K794 is invariant under the involution KW described in the page Table 62.