X3287

INTERSECTION OF LINES X44X_513 AND X523X_879

Let L denote the line through X1 parallel to the Brocard axis, X3X6. Coefficients for a trilinear equation for L are the trilinears for X3287.
< 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) { 6, 523 }: Central Line L(6, 523) { 44, 513 }: Central Line L(44, 513) { 37, 2605 }: Central Line L(37, 2605) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3907 = com[INVERSE(n(3rd EULER TRIANGLE))] (1.1014, 0.0376) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_2605 = DIFFERENCE OF PU(71) (6.1667, -1.9052) X_3287 = INTERSECTION OF LINES X(44)X(513) AND X(523)X(879) (17.0805, -6.0315) A B C X3907 X6 X523 X44 X513 X37 X2605 X3287 (a, b, c) = (5, 6, 7) | AB = 1

X3287 (INTERSECTION OF LINES X44X_513 AND X523X_879) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b - c)(b + c - a)(a^{2} + bc) : :\)
Search Value (6, 9, 13): \(-19.290793618419\)
▸ Incident Central Lines3 lines

{6, 523}, {37, 2605}, {44, 513}

▸ Functional Relations8 relations