X1110

TRILINEAR SQUARE OF X101

X1110 = crosssum of X11 and X1086
< 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) { 36, 59 }: Central Line L(36, 59) { 101, 663 }: Central Line L(101, 663) { 1, 1053 }: Central Line L(1, 1053) { 249, 849 }: Central Line L(249, 849) { 667, 692 }: Central Line L(667, 692) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1111 = TRILINEAR SQUARE OF X(514) (0.7470, 0.0849) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_1 = INCENTER (0.5714, 0.2333) X_1053 = POINT ALHENA (0.7302, -0.1555) X_249 = ISOGONAL CONJUGATE OF X(115) (0.5045, 0.3948) X_849 = 4th HATZIPOLAKIS-YIU POINT (0.6376, 0.3351) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_1110 = TRILINEAR SQUARE OF X(101) (0.5057, 0.3942) A B C X1111 X36 X59 X101 X663 X1 X1053 X249 X849 X667 X692 X1110 (a, b, c) = (5, 6, 7) | AB = 1

X1110 (TRILINEAR SQUARE OF X101) 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 \(f(a,b,c) = [a/(b - c)]^{2}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.390803181544\)
▸ Incident Central Lines5 lines

{1, 1053}, {36, 59}, {101, 663}, {249, 849}, {667, 692}

▸ Functional Relations3 relations