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X(4), X(6), X(39), X(69), X(141), X(1350), X(14994) infinite points of K102 or K141 A', B', C' : vertices of the pedal triangle of X(1350) reflections of A, B, C, X(39) about X(141) X(6)-OAP points, see Table 53 other points below |
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K805 is a central cubic with center X(141) and asymptotes parallel to those of the Grebe cubic K102. It meets the circumcircle at the same points as pK(X6, Z) where Z = X(14929) = X(5), X(183) /\ X(30), X(69) /\ X(99), X(550), etc. The reflection S = X(14994) of X(39) about X(141) lies on K805. S is also the midpoint of X(69) and X(76). It also contains the four X(6)-OAP points i.e. the points P1, P2, P3, P4 whose AntiPedal triangle has Orthocenter X(6), see also Table 53.
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These points also lie • on the cubic (K) = pK(X4 x X1350, X4) passing through X(4), X(371), X(372), X(1350), • on the rectangular hyperbola (H) passing through X(2), X(69), X(3413), X(3414), the reflection of X(39) about X(141). (H) is homothetic to the Kiepert hyperbola. |
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