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too complicated to be written here. Click on the link to download a text file. |
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X(3), X(4), X(64), X(3146) infinite points of the altitudes ZaZbZc : pedal triangle of X(64) points of pK(X6, X3146) on (O) |
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This cubic is related with Table 58. It is pK(X6, X3146)'s sister. Its isogonal transform is K426. K841 is a psK with respect to ABC with pseudo-pivot X(253) which lies on the Lucas cubic K007 hence the cevian triangle of X(253) is the pedal triangle of a point on the Darboux cubic K004, namely X(64). The pseudo-isopivot is the Lemoine point X(6) hence the tangents at A, B, C are the symmedians. K841 is also spK(X20, X4) as in CL055. See also Table 54. Recall that K841 is the isogonal pK with pivot H with respect to the triangle Q1Q2Q3 whose vertices are the intersections of (O) and pK(X6, X3146). Note that H is the centroid of Q1Q2Q3 since X(3146) is its orthocenter hence X(64) is its Lemoine point. K841 is therefore the Thomson cubic of Q1Q2Q3. It follows that ABC is the Thomson triangle of Q1Q2Q3. |