X1892

ZOSMA TRANSFORM OF X990

X1892 = X4-beth conjugate of X608
< 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, 7 }: Central Line L(4, 7) { 65, 66 }: Central Line L(65, 66) { 25, 226 }: Central Line L(25, 226) { 57, 427 }: Central Line L(57, 427) { 208, 429 }: Central Line L(208, 429) { 225, 608 }: Central Line L(225, 608) 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_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_7 = GERGONNE POINT (0.5903, 0.2769) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_429 = EULER X(58)-5th-SUBSTITUTION POINT (0.6024, 0.3700) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_1892 = ZOSMA TRANSFORM OF X(990) (0.6032, 0.3467) A B C X4 X608 X7 X65 X66 X25 X226 X57 X427 X208 X429 X225 X1892 (a, b, c) = (5, 6, 7) | AB = 1

X1892 (ZOSMA TRANSFORM OF X990) 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,\(x : y : z\) = X990
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X990
Search Value (6, 9, 13): \(1.458478428724\)
▸ Incident Central Lines12 lines

{4, 7}, {12, 1452}, {25, 226}, {33, 1836}, {57, 427}, {65, 66}, {79, 1041}, {208, 429}, {225, 608}, {388, 1829}, {1118, 1867}, {1478, 1905}

▸ Functional Relations1 relation