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X(2), X(3), X(6), X(20), X(69), X(154), X(511), X(2574), X(2575), X(3917), X(5907), X(6467), X(13414), X(13415), X(25406), X(25407), X(25408) These three latter points are the JS-images of X(3917), X(13415), X(13414), see Table 62 |
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Geometric properties : |
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K1085 is the SS{sqrt(X3)}, SS{X3}, SS{X6} image of K907, K1083, K1084 respectively. See Table 70. K1085 and K907 are two members of a pencil of isogonal pKs with respect to a non proper triangle T, namely the triangle with vertices X(511), X(13414), X(13415). This pencil contains the cubic which is the union of the line at infinity, the Brocard axis, the line X(2)X(98)X(110). See Table 62 and also the related Q149. X(3) and X(6) are the centers of two circles inscribed in T hence tangent to the line X(2)X(98)X(110). The respective pivots of K1085 and K907 are X(3917) and X(51) which are symmetric about X(2). More generally, K1085 and K907 are swapped under the oblique symmetry with axis the line X(2)X(98)X(110) and direction the Brocard axis. K1085 has three real asymptotes namely the line X(376)X(511) and the parallels at X(3917) to the asymptotes of the Jerabek hyperbola. |