X3903

X115com[INVERSE(n(3rd EULER TRIANGLE))]

X3903 = trilinear pole of line X9X43
< 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) { 99, 512 }: Central Line L(99, 512) { 256, 1320 }: Central Line L(256, 1320) { 1, 1581 }: Central Line L(1, 1581) { 1120, 1431 }: Central Line L(1120, 1431) { 1280, 1432 }: Central Line L(1280, 1432) { 257, 3057 }: Central Line L(257, 3057) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_99 = STEINER POINT (0.1109, 0.4322) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_1320 = ISOGONAL CONJUGATE OF X(1319) (1.0000, 0.0000) X_1 = INCENTER (0.5714, 0.2333) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_1120 = -BLAIKIE TRANSFORM OF X(1) (1.2041, 0.2000) X_1431 = -BETH CONJUGATE OF X(256) (0.6270, 0.3250) X_1280 = ISOGONAL CONJUGATE OF X(1279) (1.1600, 0.1306) X_1432 = -BETH CONJUGATE OF X(257) (0.6068, 0.2916) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_3057 = INTERSECTION OF LINES X(1)X(3) AND X(10)X(11) (0.5388, 0.1733) X_3903 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.0992, 0.4394) A B C X99 X512 X256 X1320 X1 X1581 X1120 X1431 X1280 X1432 X257 X3057 X3903 (a, b, c) = (5, 6, 7) | AB = 1

X3903 (X115com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(a - b)(a - c)(b^{2} + ac)(c^{2} + ab)\)
Search Value (6, 9, 13): \(3.656531121248\)
▸ Linear Combinations1 combination
▸ Incident Central Lines8 lines

{1, 1581}, {99, 512}, {256, 1320}, {257, 3057}, {643, 3573}, {893, 3744}, {1120, 1431}, {1280, 1432}

▸ Functional Relations3 relations