X1864

ZOSMA TRANSFORM OF X278

< 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) { 6, 33 }: Central Line L(6, 33) { 9, 55 }: Central Line L(9, 55) { 4, 65 }: Central Line L(4, 65) { 11, 118 }: Central Line L(11, 118) { 44, 212 }: Central Line L(44, 212) { 72, 519 }: Central Line L(72, 519) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) 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_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_1864 = ZOSMA TRANSFORM OF X(278) (0.5992, 0.2325) A B C X6 X33 X9 X55 X4 X65 X11 X118 X44 X212 X72 X519 X1864 (a, b, c) = (5, 6, 7) | AB = 1

X1864 (ZOSMA TRANSFORM OF X278) 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,\(x : y : z\) = X278
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X278
Search Value (6, 9, 13): \(2.126213959661\)
▸ Incident Central Lines22 lines

{3, 1728}, {4, 65}, {6, 33}, {9, 55}, {11, 118}, {44, 212}, {51, 1824}, {56, 1490}, {57, 971}, {72, 519}, {84, 1466}, {227, 774}, {329, 497}, {381, 942}, {389, 1872}, {405, 997}, {430, 1827}, {452, 960}, {1005, 1776}, {1155, 1708}, {1210, 1532}, {1214, 1736}

▸ Functional Relations3 relations