X1177

1st SARAGOSSA POINT OF X67

X1177 = trilinear pole of line X32X647
< 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) { 69, 110 }: Central Line L(69, 110) { 66, 125 }: Central Line L(66, 125) { 67, 468 }: Central Line L(67, 468) { 68, 542 }: Central Line L(68, 542) { 72, 692 }: Central Line L(72, 692) { 23, 895 }: Central Line L(23, 895) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_858 = COMPLEMENT OF X(23) (0.1126, -0.9116) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_67 = ISOGONAL CONJUGATE OF X(23) (0.7606, -0.2152) X_468 = -LINE CONJUGATE OF X(3) (0.7498, 0.7558) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_542 = DIRECTION OF VECTOR AX + BX + CX, where X = X(98) (0.1649, 0.6534) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_895 = ISOGONAL CONJUGATE OF X(468) (0.9484, -0.0134) X_1177 = 1st SARAGOSSA POINT OF X(67) (0.7694, -1.0073) A B C X858 X69 X110 X66 X125 X67 X468 X68 X542 X72 X692 X23 X895 X1177 (a, b, c) = (5, 6, 7) | AB = 1

X1177 (1st SARAGOSSA POINT OF X67) 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 \(f(a,b,c) = a/(b^{6} + c^{6} - a^{4}b^{2} - a^{4}c^{2} + 2a^{2}b^{2}c^{2} - b^{4}c^{2} - b^{2}c^{4})\) (M. Iliev, 5/25/07)
Search Value (6, 9, 13): \(-2.660044971196\)
▸ Incident Central Lines8 lines

{6, 1112}, {23, 895}, {66, 125}, {67, 468}, {68, 542}, {69, 110}, {72, 692}, {290, 685}

▸ Functional Relations8 relations

Notes

See Angel Montesdeoca, Hyacinthos #21528, 2/12/2013