X1905

ZOSMA TRANSFORM OF X1478

X1905 = reflection of X222 in X942
< 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) { 222, 942 }: Central Line L(222, 942) { 1, 25 }: Central Line L(1, 25) { 4, 65 }: Central Line L(4, 65) { 34, 222 }: Central Line L(34, 222) { 33, 517 }: Central Line L(33, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_1 = INCENTER (0.5714, 0.2333) 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_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1905 = ZOSMA TRANSFORM OF X(1478) (0.6102, 0.3698) A B C X222 X942 X1 X25 X4 X65 X34 X33 X517 X1905 (a, b, c) = (5, 6, 7) | AB = 1

X1905 (ZOSMA TRANSFORM OF X1478) 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,\(x : y : z\) = X1478
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X1478
Search Value (6, 9, 13): \(3.526084553284\)
▸ Incident Central Lines21 lines

{1, 25}, {3, 1452}, {4, 65}, {33, 517}, {34, 222}, {46, 1593}, {52, 1866}, {169, 607}, {225, 1831}, {354, 1870}, {378, 1155}, {406, 960}, {427, 1737}, {1426, 1838}, {1478, 1892}, {1730, 1735}, {1770, 1885}, {1785, 1824}, {1825, 1872}, {1827, 1845}, {1828, 1844}

▸ Functional Relations3 relations