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K1106

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X(3), X(6), X(74), X(110), X(511), X(1113), X(1114), X(1495), X(2574), X(2575), X(13414), X(13415)

S3, S4 common points of the line X(74), X(99) and the Stammler hyperbola (S)

Geometric properties :

K1106 is JSpK(X1495) in Table 62. It is an example of pK with respect to a non proper triangle T, namely the triangle with vertices S1 = X(13414), S2 = X(13415), X(511). See also K907, K1107 and the related Q149.

It has three real asymptotes, namely the parallel at X(74) to the Brocard axis and the parallels at X(1495) to those of the Jerabek hyperbola (J).

K1106 is invariant under the quadratic involution JS mentioned in Table 62 which may be seen as the isogonal conjugation in T. Its pivot is X(1495) and its isopivot is X(74).

Remarkable polar conics C(P) of some points P with respect to K1106 :

• C(X6) passing through X(6), X(69), X(74), X(110), X(1113), X(1114), X(1350), with center X(3),

• C(X74) passing through X(74), X(511), X(1495), X(2777), X(13414), X(13415),

• C(X1495) passing through X(3), X(6), X(468), X(647), X(1495), X(2574), X(2575), a rectangular hyperbola labelled (H) below.

Note that the tangentials of X(1495), X(74), X(6) are X(74), X(6), X(1495) respectively.

K1106a