X3004

(DE LONGCHAMPS LINE)∩(GERGONNE LINE)

X3004 = crossdifference of every pair of points on line X32X55
< 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) { 241, 514 }: Central Line L(241, 514) { 325, 523 }: Central Line L(325, 523) { 661, 918 }: Central Line L(661, 918) { 522, 2526 }: Central Line L(522, 2526) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (37.2857, -17.0298) X_3004 = (DE LONGCHAMPS LINE)∩(GERGONNE LINE) (51.8776, -20.6957) A B C X241 X514 X325 X523 X661 X918 X522 X2526 X3004 (a, b, c) = (5, 6, 7) | AB = 1

X3004 ((DE LONGCHAMPS LINE)∩(GERGONNE LINE)) 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 \(f(a,b,c) = bc(b - c)(b^{2} + c^{2} + ab + ac)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-71.744205623621\)
▸ Incident Central Lines4 lines

{241, 514}, {325, 523}, {522, 2526}, {661, 918}

▸ Functional Relations5 relations