X1859

ZOSMA TRANSFORM OF X226

X1859 = crosssum of X3 and X1214
< 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) { 19, 25 }: Central Line L(19, 25) { 4, 65 }: Central Line L(4, 65) { 11, 132 }: Central Line L(11, 132) { 27, 243 }: Central Line L(27, 243) { 210, 281 }: Central Line L(210, 281) { 92, 518 }: Central Line L(92, 518) 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_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_4 = ORTHOCENTER (0.6122, 0.3958) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_132 = ∩X(4)X(32) (0.5642, 0.5039) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1859 = ZOSMA TRANSFORM OF X(226) (0.6113, 0.3833) A B C X19 X25 X4 X65 X11 X132 X27 X243 X210 X281 X92 X518 X1859 (a, b, c) = (5, 6, 7) | AB = 1

X1859 (ZOSMA TRANSFORM OF X226) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((y + z) \sec A : (z + x) \sec B : (x + y) \sec C\), where \(x : y : z\) = X226
Barycentrics: \((y + z) \tan A : (z + x) \tan B : (x + y) \tan C\), where \(x : y : z\) = X226
Search Value (6, 9, 13): \(16.924836039054\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\tan A [(b + c) \cos A + b \cos B + c \cos C] : :\)

▸ Incident Central Lines18 lines

{1, 1871}, {4, 65}, {6, 1096}, {11, 132}, {19, 25}, {27, 243}, {29, 960}, {40, 1872}, {92, 518}, {209, 1826}, {210, 281}, {278, 354}, {942, 1838}, {950, 1852}, {1013, 1748}, {1825, 1902}, {1829, 1831}, {1869, 1894}

▸ Functional Relations3 relations