X1830

ZOSMA TRANSFORM OF X11

X1830 = polar conjugate of isogonal conjugate of X21742
< 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, 80 }: Central Line L(4, 80) { 33, 57 }: Central Line L(33, 57) { 65, 1846 }: Central Line L(65, 1846) { 225, 1872 }: Central Line L(225, 1872) { 517, 1877 }: Central Line L(517, 1877) { 900, 1862 }: Central Line L(900, 1862) 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_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1846 = ZOSMA TRANSFORM OF X(104) (0.5566, 0.5453) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_1872 = ZOSMA TRANSFORM OF X(499) (0.6365, 0.4403) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1877 = ZOSMA TRANSFORM OF X(517) (0.6803, 0.6665) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (0.9566, 0.6107) X_1862 = ZOSMA TRANSFORM OF X(244) (0.5569, 0.4523) X_1830 = ZOSMA TRANSFORM OF X(11) (0.5714, 0.4666) A B C X4 X80 X33 X57 X65 X1846 X225 X1872 X517 X1877 X900 X1862 X1830 (a, b, c) = (5, 6, 7) | AB = 1

X1830 (ZOSMA TRANSFORM OF X11) 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,\(x : y : z\) = X11
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X11
Search Value (6, 9, 13): \(-1.644478251356\)
▸ Incident Central Lines10 lines

{4, 80}, {33, 57}, {65, 1846}, {225, 1872}, {517, 1877}, {900, 1862}, {908, 1861}, {1785, 1835}, {1887, 1902}, {1888, 1900}

▸ Functional Relations1 relation

  • X1830 = polar conjugate of isogonal conjugate of X21742