X1848

ZOSMA TRANSFORM OF X171

X1848 = crosspoint of X27 and X92
< 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, 4 }: Incenter–Orthocenter Line { 2, 19 }: Central Line L(2, 19) { 27, 86 }: Central Line L(27, 86) { 11, 132 }: Central Line L(11, 132) { 92, 264 }: Central Line L(92, 264) { 286, 350 }: Central Line L(286, 350) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_2 = CENTROID (0.5374, 0.2000) X_19 = CLAWSON POINT (0.6246, 0.4244) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_132 = ∩X(4)X(32) (0.5642, 0.5039) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_286 = -CROSS CONJUGATE OF X(27) (0.6033, 0.3810) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_1848 = ZOSMA TRANSFORM OF X(171) (0.6100, 0.3866) A B C X27 X92 X1 X4 X2 X19 X86 X11 X132 X264 X286 X350 X1848 (a, b, c) = (5, 6, 7) | AB = 1

X1848 (ZOSMA TRANSFORM OF X171) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X171
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X171
Search Value (6, 9, 13): \(-11.905551328314\)
▸ Incident Central Lines17 lines

{1, 4}, {2, 19}, {5, 1871}, {7, 1435}, {11, 132}, {25, 1001}, {27, 86}, {28, 1125}, {29, 1842}, {92, 264}, {286, 350}, {427, 1824}, {429, 960}, {608, 940}, {1595, 1872}, {1828, 1904}, {1883, 1900}

▸ Functional Relations6 relations