X1878

ZOSMA TRANSFORM OF X519

X1878 = inverse-in-polar-circle of X8
< 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, 8 }: Fuhrmann Line { 25, 36 }: Central Line L(25, 36) { 428, 535 }: Central Line L(428, 535) { 34, 1319 }: Central Line L(34, 1319) { 855, 1465 }: Central Line L(855, 1465) { 513, 1835 }: Central Line L(513, 1835) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1811 = INVERSE MIMOSA TRANSFORM OF X(519) (1.5714, 0.1077) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_428 = EULER X(38)-5th-SUBSTITUTION POINT (0.6180, 0.4109) X_535 = DIRECTION OF VECTOR AX + BX + CX, where X = X(36) (0.8224, 0.7130) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_855 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(57) (0.8408, 0.9939) X_1465 = -BETH CONJUGATE OF X(908) (0.7719, 1.0314) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1835 = ZOSMA TRANSFORM OF X(30) (0.6564, 0.6795) X_1878 = ZOSMA TRANSFORM OF X(519) (0.7415, 0.6332) A B C X1811 X4 X8 X25 X36 X428 X535 X34 X1319 X855 X1465 X513 X1835 X1878 (a, b, c) = (5, 6, 7) | AB = 1

X1878 (ZOSMA TRANSFORM OF X519) 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,\(x : y : z\) = X519
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X519
Search Value (6, 9, 13): \(0.873834106305\)
▸ Incident Central Lines10 lines

{4, 8}, {25, 36}, {34, 1319}, {428, 535}, {513, 1835}, {519, 1862}, {855, 1465}, {1318, 1870}, {1842, 1888}, {1866, 1887}

▸ Functional Relations4 relations