X1839

ZOSMA TRANSFORM OF X37

X1839 = X4-Ceva conjugate of X430
< 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, 9 }: Orthocenter–Spieker Line { 27, 86 }: Central Line L(27, 86) { 225, 608 }: Central Line L(225, 608) { 52, 916 }: Central Line L(52, 916) { 48, 946 }: Central Line L(48, 946) { 79, 1172 }: Central Line L(79, 1172) 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_430 = EULER X(81)-5th-SUBSTITUTION POINT (0.6091, 0.3875) X_9 = MITTENPUNKT (0.5110, 0.1615) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_916 = -CEVA CONJUGATE OF X(3) (0.0224, -0.0814) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_1839 = ZOSMA TRANSFORM OF X(37) (0.6155, 0.4034) A B C X4 X430 X9 X27 X86 X225 X608 X52 X916 X48 X946 X79 X1172 X1839 (a, b, c) = (5, 6, 7) | AB = 1

X1839 (ZOSMA TRANSFORM OF X37) 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,\(x : y : z\) = X37
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X37
Search Value (6, 9, 13): \(-3.784015460002\)
▸ Incident Central Lines18 lines

{4, 9}, {6, 1836}, {27, 86}, {48, 946}, {52, 916}, {79, 1172}, {193, 3187}, {225, 608}, {278, 1419}, {430, 1213}, {534, 1441}, {579, 1770}, {610, 1699}, {674, 1824}, {1831, 1858}, {1840, 1900}, {1841, 1852}, {1877, 1880}

▸ Functional Relations5 relations