X1858

ZOSMA TRANSFORM OF X225

X1858 = crosspoint of X4 and X21
< 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, 65 }: Central Line L(4, 65) { 21, 60 }: Central Line L(21, 60) { 1, 90 }: Central Line L(1, 90) { 11, 113 }: Central Line L(11, 113) { 55, 72 }: Central Line L(55, 72) { 144, 145 }: Central Line L(144, 145) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_1 = INCENTER (0.5714, 0.2333) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_1858 = ZOSMA TRANSFORM OF X(225) (0.6003, 0.2464) A B C X4 X21 X65 X60 X1 X90 X11 X113 X55 X72 X144 X145 X1858 (a, b, c) = (5, 6, 7) | AB = 1

X1858 (ZOSMA TRANSFORM OF X225) 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,\(x : y : z\) = X225
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X225
Search Value (6, 9, 13): \(1.944278045569\)
▸ Incident Central Lines14 lines

{1, 90}, {3, 920}, {4, 65}, {6, 1854}, {11, 113}, {21, 60}, {52, 517}, {55, 72}, {73, 774}, {144, 145}, {411, 1155}, {758, 950}, {1829, 1852}, {1831, 1839}

▸ Functional Relations4 relations