X1909

CROSSSUM OF PU(9)

X1909 = anticomplement of X1107
< 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) { 7, 8 }: Gergonne–Nagel Line { 1, 76 }: Central Line L(1, 76) { 35, 99 }: Central Line L(35, 99) { 56, 183 }: Central Line L(56, 183) { 10, 274 }: Central Line L(10, 274) { 34, 264 }: Central Line L(34, 264) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_1 = INCENTER (0.5714, 0.2333) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_99 = STEINER POINT (0.1109, 0.4322) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_1909 = CROSSSUM OF PU(9) (0.5132, 0.1854) A B C X904 X7 X8 X1 X76 X35 X99 X56 X183 X10 X274 X34 X264 X1909 (a, b, c) = (5, 6, 7) | AB = 1

X1909 (CROSSSUM OF PU(9)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1 + bc/a^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.334632005267\)
▸ Incident Central Lines25 lines

{1, 76}, {2, 330}, {7, 8}, {10, 274}, {12, 325}, {34, 264}, {35, 99}, {36, 1078}, {37, 1655}, {42, 310}, {56, 183}, {73, 290}, {86, 313}, {172, 385}, {190, 1334}, {226, 1432}, {256, 1221}, {257, 335}, {286, 1891}, {305, 612}, {315, 1478}, {538, 1500}, {732, 894}, {1215, 1237}, {1235, 1870}

▸ Functional Relations8 relations