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K1107

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X(3), X(6), X(54), X(74), X(186), X(511), X(1495), X(2574), X(2575), X(2931), X(5621), X(12584), X(13414), X(13415), X(15462), X(32352)

other points below

Geometric properties :

K1107 is JSpK(X186) 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, K1106 and the related Q149.

It has three real asymptotes, namely the parallel at X(2071) to the Brocard axis and the parallels at X(186) to those of the Jerabek hyperbola (J).

K1107 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(186) and its isopivot is P3 = X(32607), the common tangential of X(186), X(511), S1, S2. P3 is the intersection of the lines {3,125},{54,74}, {511,2071}, {186,13851}, etc, and note that the first (light blue) line is the polar of X(186) in the Stammler hyperbola (S).

K1107a

Other centers on K1107 :

P4 = X(32608) on the lines {3, 54}, {30, 3448}, {52, 14130}, {74, 13391}, {185, 13564}, {323, 15646}, {381, 17810}, {382, 9927}, {389, 15047}, {399, 1495}, {511, 5621}, etc.

P5 = X(32609) = JS(P4) on the lines {2, 11694}, {3, 74}, {4, 7666}, {5, 12383}, {6, 11935}, {20, 20125}, {24, 3043}, {25, 15463}, {40, 11699}, {49, 9730}, {54, 5898}, {64, 25564}, {113, 382}, {125, 3526}, etc.

P6 = X(32598) on the lines {54, 511}, {2916, 2931}, {7488, 29012}, {9019, 19129}, {13564, 32351}, etc.

P7 = X(32599) = JS(X12584) on the lines {3, 524}, {23, 542}, {30, 16010}, {54, 20190}, {68, 7530}, {74, 511}, {110, 32315}, {182, 323}, {186, 12584}, {399, 32217}, etc.

P8 = X(32600) = JS(P6) on the lines {3, 2916}, {74, 827}, {141, 12901}, {182, 7689}, {206, 3357}, {511, 7691}, {549, 13289}, {1352, 16013}, {1495, 5888}, {1503, 32401}, {1531, 7550}, {1843, 3520}, {3098, 9019}, {5085, 11999}, {7512, 29323}, {8718, 15030}, {10226, 21167}, {14130, 29317}, {20190, 21637}, etc.

X(32620) on the lines {3, 1495}, {5, 4549}, {6, 32599}, {22, 16261}, {30, 10516}, {54, 155}, {64, 7516}, {140, 3532}, {154, 15060}, etc.

X(32621) on the lines {3, 524}, {6, 25}, {22, 1992}, {23, 5032}, {24, 11431}, {67, 32240}, {69, 7485}, {140, 9925}, etc.