X158

X19-CROSS CONJUGATE OF X92

X158 = X107-beth conjugate of X34
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 29 }: Central Line L(1, 29) { 4, 65 }: Central Line L(4, 65) { 47, 162 }: Central Line L(47, 162) { 3, 243 }: Central Line L(3, 243) { 75, 240 }: Central Line L(75, 240) { 37, 281 }: Central Line L(37, 281) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_19 = CLAWSON POINT (0.6246, 0.4244) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1 = INCENTER (0.5714, 0.2333) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_4 = ORTHOCENTER (0.6122, 0.3958) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) A B C X19 X92 X1 X29 X4 X65 X47 X162 X3 X243 X75 X240 X37 X281 X158 (a, b, c) = (5, 6, 7) | AB = 1

X158 (X19-CROSS CONJUGATE OF X92) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec^{2} A : \sec^{2} B : \sec^{2} C\)
Barycentrics: \(\sec A \tan A : \sec B \tan B : \sec C \tan C\)
Search Value (6, 9, 13): \(0.730217888460\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1/(1 + \cos 2A) : 1/(1 + \cos 2B) : 1/(1 + \cos 2C)\)

▸ Incident Central Lines15 lines

{1, 29}, {3, 243}, {4, 65}, {10, 318}, {37, 281}, {46, 412}, {47, 162}, {75, 240}, {107, 759}, {225, 1093}, {255, 775}, {286, 969}, {823, 897}, {920, 921}, {1068, 3542}

▸ Functional Relations12 relations

Notes

Let A'B'C' be the hexyl triangle. Let A″ be the pole, wrt the polar circle, of line B'C', and define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X158. (Randy Hutson, October 15, 2018)

Let A'B'C' and A″B″C″ be the Euler and anti-Euler triangles, resp. Let A* be the trilinear product A'*A″, and define B* and C* cyclically. The lines AA*, BB*, CC* concur in X158. (Randy Hutson, October 15, 2018)