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K1108

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X(3), X(4), X(6), X(20), X(64), X(185), X(511), X(2574), X(2575), X(5907), X(5921), X(11381), X(12164), X(13414), X(13415)

other points below

Geometric properties :

K1108 is JSpK(X11381) 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, K1107 and the related Q149.

It has three real asymptotes, namely the parallel at X = X(32601) = JS(X11381) to the Brocard axis and the parallels at X(11381) to those of the Jerabek hyperbola (J). Note that X lies on the (green) polar of X(11381) in the Stammler hyperbola (S).

K1108 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(11381) and its isopivot is X, the common tangential of X(11381), X(511), S1, S2. X is the intersection of the lines {4, 64}, {20,12164}, etc.

Other centers on K1108 :

• T1 = X(32602) = JS(X64), on the lines {54,11381}, {511,12164},

• T2 = X(32603) common tangential of X(185), X(5907), on the line {3,5921},

• T3 = X(32604) = JS(X12164), on the line {11381,12164},

• T4 = X(32605) = X(4)– Ceva conjugate of X(20), on the lines {X2,X185}, {X4,X3167}, {X6,X3091}, {X20,X154}, {X52,X3089}, {110,3146}.

K1108a