X1851

ZOSMA TRANSFORM OF X200

X1851 = X4-Ceva conjugate of X1863
< 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) { 4, 8 }: Fuhrmann Line { 25, 105 }: Central Line L(25, 105) { 34, 207 }: Central Line L(34, 207) { 2, 242 }: Central Line L(2, 242) { 286, 310 }: Central Line L(286, 310) { 19, 672 }: Central Line L(19, 672) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1863 = ZOSMA TRANSFORM OF X(269) (0.6414, 0.4494) X_8 = NAGEL POINT (0.4694, 0.1333) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_2 = CENTROID (0.5374, 0.2000) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) X_286 = -CROSS CONJUGATE OF X(27) (0.6033, 0.3810) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_19 = CLAWSON POINT (0.6246, 0.4244) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1851 = ZOSMA TRANSFORM OF X(200) (0.6375, 0.4422) A B C X4 X1863 X8 X25 X105 X34 X207 X2 X242 X286 X310 X19 X672 X1851 (a, b, c) = (5, 6, 7) | AB = 1

X1851 (ZOSMA TRANSFORM OF X200) 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,\(x : y : z\) = X200
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X200
Search Value (6, 9, 13): \(-0.899158827940\)
▸ Incident Central Lines12 lines

{2, 242}, {4, 8}, {19, 672}, {25, 105}, {34, 207}, {196, 1876}, {281, 427}, {286, 310}, {479, 1119}, {497, 1863}, {1146, 1853}, {1395, 1430}

▸ Functional Relations4 relations