X1894

ZOSMA TRANSFORM OF X993

< 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 { 19, 53 }: Central Line L(19, 53) { 225, 1829 }: Central Line L(225, 1829) { 1785, 1824 }: Central Line L(1785, 1824) { 1828, 1838 }: Central Line L(1828, 1838) { 1859, 1869 }: Central Line L(1859, 1869) 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_19 = CLAWSON POINT (0.6246, 0.4244) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_1829 = ZOSMA TRANSFORM OF X(10) (0.6233, 0.4161) X_1785 = MIMOSA TRANSFORM OF X(1295) (0.7297, 0.8635) X_1824 = ZOSMA TRANSFORM OF X(2) (0.6198, 0.4097) X_1828 = ZOSMA TRANSFORM OF X(8) (0.6327, 0.4332) X_1838 = ZOSMA TRANSFORM OF X(35) (0.6188, 0.4218) X_1859 = ZOSMA TRANSFORM OF X(226) (0.6113, 0.3833) X_1869 = ZOSMA TRANSFORM OF X(405) (0.6206, 0.4150) X_1894 = ZOSMA TRANSFORM OF X(993) (0.6238, 0.4259) A B C X2 X3 X4 X19 X53 X225 X1829 X1785 X1824 X1828 X1838 X1859 X1869 X1894 (a, b, c) = (5, 6, 7) | AB = 1

X1894 (ZOSMA TRANSFORM OF X993) 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,\(x : y : z\) = X993
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X993
Search Value (6, 9, 13): \(-1.271591791725\)
▸ Incident Central Lines6 lines

{2, 3}, {19, 53}, {225, 1829}, {1785, 1824}, {1828, 1838}, {1859, 1869}

Notes

As a point on the Euler line, X1894 has Shinagawa coefficients \((\$a\$F, -2\$aS_{A}\$ - \$a\$(E + F))\).