X1828

ZOSMA TRANSFORM OF X8

X1828 = crosspoint of X4 and 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) { 4, 8 }: Fuhrmann Line { 25, 34 }: Central Line L(25, 34) { 19, 44 }: Central Line L(19, 44) { 28, 88 }: Central Line L(28, 88) { 51, 65 }: Central Line L(51, 65) { 428, 529 }: Central Line L(428, 529) 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_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_8 = NAGEL POINT (0.4694, 0.1333) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_19 = CLAWSON POINT (0.6246, 0.4244) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) 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_1828 = ZOSMA TRANSFORM OF X(8) (0.6327, 0.4332) A B C X4 X34 X8 X25 X19 X44 X28 X88 X51 X65 X428 X529 X1828 (a, b, c) = (5, 6, 7) | AB = 1

X1828 (ZOSMA TRANSFORM OF X8) 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,\(x : y : z\) = X8
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X8
Search Value (6, 9, 13): \(-1.059879109114\)
▸ Incident Central Lines14 lines

{4, 8}, {10, 1883}, {19, 44}, {25, 34}, {28, 88}, {46, 1707}, {51, 65}, {225, 1846}, {427, 1329}, {428, 529}, {1827, 1843}, {1838, 1894}, {1844, 1884}, {1848, 1904}

▸ Functional Relations4 relations