X1904

ZOSMA TRANSFORM OF X1468

< 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) { 2, 3 }: Euler Line { 12, 968 }: Central Line L(12, 968) { 80, 1039 }: Central Line L(80, 1039) { 53, 1826 }: Central Line L(53, 1826) { 10, 1900 }: Central Line L(10, 1900) { 1785, 1867 }: Central Line L(1785, 1867) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_968 = POINT ALDERAMIN (0.5557, 0.2126) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1039 = ISOGONAL CONJUGATE OF X(1038) (0.6094, 0.3672) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_1826 = ZOSMA TRANSFORM OF X(6) (0.6052, 0.3795) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1900 = ZOSMA TRANSFORM OF X(1125) (0.6180, 0.4064) X_1785 = MIMOSA TRANSFORM OF X(1295) (0.7297, 0.8635) X_1867 = ZOSMA TRANSFORM OF X(386) (0.6074, 0.3868) X_1904 = ZOSMA TRANSFORM OF X(1468) (0.6044, 0.3753) A B C X2 X3 X4 X12 X968 X80 X1039 X53 X1826 X10 X1900 X1785 X1867 X1904 (a, b, c) = (5, 6, 7) | AB = 1

X1904 (ZOSMA TRANSFORM OF X1468) 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,\(x : y : z\) = X1468
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X1468
Search Value (6, 9, 13): \(-161.920265180649\)
▸ Incident Central Lines7 lines

{2, 3}, {10, 1900}, {12, 968}, {53, 1826}, {80, 1039}, {1785, 1867}, {1828, 1848}

Notes

As a point on the Euler line, X1904 has Shinagawa coefficients \((FS^{2}, -(E - F)S^{2} - 2\$bc\$S^{2} + 2\$bcS_{B}S_{C}\$)\).