X1862

ZOSMA TRANSFORM OF X244

< 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) { 11, 33 }: Central Line L(11, 33) { 25, 100 }: Central Line L(25, 100) { 4, 145 }: Central Line L(4, 145) { 119, 235 }: Central Line L(119, 235) { 428, 528 }: Central Line L(428, 528) { 80, 1039 }: Central Line L(80, 1039) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_4 = ORTHOCENTER (0.6122, 0.3958) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_235 = -CEVA CONJUGATE OF X(185) (0.6375, 0.4618) X_428 = EULER X(38)-5th-SUBSTITUTION POINT (0.6180, 0.4109) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1039 = ISOGONAL CONJUGATE OF X(1038) (0.6094, 0.3672) X_1862 = ZOSMA TRANSFORM OF X(244) (0.5569, 0.4523) A B C X11 X33 X25 X100 X4 X145 X119 X235 X428 X528 X80 X1039 X1862 (a, b, c) = (5, 6, 7) | AB = 1

X1862 (ZOSMA TRANSFORM OF X244) 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,\(x : y : z\) = X244
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X244
Search Value (6, 9, 13): \(-2.750206567129\)
▸ Incident Central Lines13 lines

{4, 145}, {11, 33}, {25, 100}, {34, 1317}, {80, 1039}, {104, 1593}, {119, 235}, {428, 528}, {468, 1861}, {519, 1878}, {900, 1830}, {1387, 1883}, {1484, 1595}