X1891

ZOSMA TRANSFORM OF X986

X1891 = polar conjugate of isotomic conjugate of complement of X27184
< 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 { 8, 19 }: Central Line L(8, 19) { 10, 28 }: Central Line L(10, 28) { 27, 306 }: Central Line L(27, 306) { 428, 529 }: Central Line L(428, 529) { 25, 958 }: Central Line L(25, 958) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_19 = CLAWSON POINT (0.6246, 0.4244) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_428 = EULER X(38)-5th-SUBSTITUTION POINT (0.6180, 0.4109) X_529 = DIRECTION OF VECTOR AX + BX + CX, where X = X(12) (0.8589, 0.6909) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_1891 = ZOSMA TRANSFORM OF X(986) (0.6148, 0.4060) A B C X1 X4 X8 X19 X10 X28 X27 X306 X428 X529 X25 X958 X1891 (a, b, c) = (5, 6, 7) | AB = 1

X1891 (ZOSMA TRANSFORM OF X986) 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,\(x : y : z\) = X986
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X986
Search Value (6, 9, 13): \(-3.361937217888\)
▸ Incident Central Lines12 lines

{1, 4}, {8, 19}, {10, 28}, {25, 958}, {27, 306}, {29, 1220}, {65, 1503}, {92, 1842}, {428, 529}, {518, 1829}, {952, 1871}, {1867, 1884}

▸ Functional Relations1 relation

  • X1891 = polar conjugate of isotomic conjugate of complement of X27184