X1883

ZOSMA TRANSFORM OF X595

< 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 { 10, 1828 }: Central Line L(10, 1828) { 12, 1877 }: Central Line L(12, 1877) { 1387, 1862 }: Central Line L(1387, 1862) { 1829, 1861 }: Central Line L(1829, 1861) { 1848, 1900 }: Central Line L(1848, 1900) 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_10 = SPIEKER CENTER (0.5204, 0.1833) X_1828 = ZOSMA TRANSFORM OF X(8) (0.6327, 0.4332) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1877 = ZOSMA TRANSFORM OF X(517) (0.6803, 0.6665) X_1387 = MIDPOINT OF INCENTER AND FEUERBACH POINT (0.6531, 0.1500) X_1862 = ZOSMA TRANSFORM OF X(244) (0.5569, 0.4523) X_1829 = ZOSMA TRANSFORM OF X(10) (0.6233, 0.4161) X_1861 = ZOSMA TRANSFORM OF X(238) (0.8061, 0.8443) X_1848 = ZOSMA TRANSFORM OF X(171) (0.6100, 0.3866) X_1900 = ZOSMA TRANSFORM OF X(1125) (0.6180, 0.4064) X_1883 = ZOSMA TRANSFORM OF X(595) (0.5918, 0.3424) A B C X2 X3 X4 X10 X1828 X12 X1877 X1387 X1862 X1829 X1861 X1848 X1900 X1883 (a, b, c) = (5, 6, 7) | AB = 1

X1883 (ZOSMA TRANSFORM OF X595) 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,\(x : y : z\) = X595
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X595
Search Value (6, 9, 13): \(8.212288102464\)
▸ Incident Central Lines6 lines

{2, 3}, {10, 1828}, {12, 1877}, {1387, 1862}, {1829, 1861}, {1848, 1900}

Notes

As a point on the Euler line, X1883 has Shinagawa coefficients \((\$a\$F, \$a\$(E + F) - 2abc)\).