X1877

ZOSMA TRANSFORM OF X517

X1877 = X4-Ceva conjugate of X1846
< 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) { 1, 4 }: Incenter–Orthocenter Line { 51, 65 }: Central Line L(51, 65) { 11, 1455 }: Central Line L(11, 1455) { 25, 1470 }: Central Line L(25, 1470) { 30, 1465 }: Central Line L(30, 1465) { 603, 1210 }: Central Line L(603, 1210) 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_1846 = ZOSMA TRANSFORM OF X(104) (0.5566, 0.5453) X_1 = INCENTER (0.5714, 0.2333) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1455 = -BETH CONJUGATE OF X(515) (0.6407, 1.1028) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_1470 = -BETH CONJUGATE OF X(997) (0.5950, 0.2766) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1465 = -BETH CONJUGATE OF X(908) (0.7719, 1.0314) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_1210 = ISOGONAL CONJUGATE OF X(1167) (0.6144, 0.2754) X_1877 = ZOSMA TRANSFORM OF X(517) (0.6803, 0.6665) A B C X4 X1846 X1 X51 X65 X11 X1455 X25 X1470 X30 X1465 X603 X1210 X1877 (a, b, c) = (5, 6, 7) | AB = 1

X1877 (ZOSMA TRANSFORM OF X517) 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,\(x : y : z\) = X517
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X517
Search Value (6, 9, 13): \(0.210397116841\)
▸ Incident Central Lines18 lines

{1, 4}, {11, 1455}, {12, 1883}, {25, 1470}, {30, 1465}, {51, 65}, {109, 1737}, {221, 1837}, {513, 1835}, {517, 1830}, {603, 1210}, {608, 1826}, {751, 1890}, {765, 1861}, {1319, 1846}, {1707, 1788}, {1825, 1829}, {1839, 1880}

▸ Functional Relations3 relations