X2648

TRILINEAR POLE OF PU(80)

X2648 = isogonal conjugate of X1758
< 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, 1046 }: Central Line L(4, 1046) { 80, 1757 }: Central Line L(80, 1757) { 896, 1156 }: Central Line L(896, 1156) { 21, 2310 }: Central Line L(21, 2310) { 851, 1758 }: Central Line L(851, 1758) { 651, 2647 }: Central Line L(651, 2647) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1758 = MIMOSA TRANSFORM OF X(296) (1.1982, 1.3847) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1757 = MIMOSA TRANSFORM OF X(295) (2.6667, 2.7217) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (2.0357, 2.1579) X_1156 = ISOGONAL CONJUGATE OF X(1155) (0.8791, -0.1436) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_2310 = -ISOCONJUGATE OF X(1262) (0.7196, 0.0518) X_851 = -HIRST INVERSE OF X(73) (1.4149, 2.4958) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_2647 = CROSSSUM OF PU(80) (0.5810, 0.2715) X_2648 = TRILINEAR POLE OF PU(80) (0.9134, -0.0753) A B C X1758 X4 X1046 X80 X1757 X896 X1156 X21 X2310 X851 X651 X2647 X2648 (a, b, c) = (5, 6, 7) | AB = 1

X2648 (TRILINEAR POLE OF PU(80)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[(\cos A + \cos B)(\cos A + \cos C) - (\cos B + \cos C)^{2}]\)
Search Value (6, 9, 13): \(2.414672341547\)
▸ Alternate Coordinates1 form

  • Trilinears: \((a - b - c)/(a^{3} + b^{3} + c^{3} - 2 a^{2} (b + c) + a b c) : :\)

▸ Incident Central Lines7 lines

{1, 2652}, {4, 1046}, {21, 2310}, {80, 1757}, {651, 2647}, {851, 1758}, {896, 1156}

▸ Functional Relations1 relation