X1941

CROSSSUM OF PU(17)

X1941 = X1942-Ceva conjugate of X450
< 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, 155 }: Central Line L(4, 155) { 185, 648 }: Central Line L(185, 648) { 3, 1075 }: Central Line L(3, 1075) { 450, 1092 }: Central Line L(450, 1092) { 194, 1593 }: Central Line L(194, 1593) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1942 = TRILINEAR POLE OF U(17) (0.8014, -0.1046) X_450 = -HIRST INVERSE OF X(4) (0.8978, 1.1430) X_4 = ORTHOCENTER (0.6122, 0.3958) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1075 = -CEVA CONJUGATE OF X(4) (0.6630, 1.7036) X_1092 = TRILINEAR CUBE OF X(3) (0.3503, 0.0118) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_1593 = POINT CEBALRAI (0.5972, 0.3563) X_1941 = CROSSSUM OF PU(17) (0.5282, 0.3794) A B C X1942 X450 X4 X155 X185 X648 X3 X1075 X1092 X194 X1593 X1941 (a, b, c) = (5, 6, 7) | AB = 1

X1941 (CROSSSUM OF PU(17)) 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 \(f(a,b,c) = \cos B \cos C (\cos^{4} A + \cos^{2} B \cos^{2} C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-12.678331409969\)
▸ Incident Central Lines5 lines

{3, 1075}, {4, 155}, {185, 648}, {194, 1593}, {450, 1092}

▸ Functional Relations3 relations