X540

DIRECTION OF VECTOR AX + BX + CX, where X = X58

< 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) { 2, 58 }: Central Line L(2, 58) { 30, 511 }: Central Line L(30, 511) { 340, 447 }: Central Line L(340, 447) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_340 = ISOTOMIC CONJUGATE OF X(265) (1.2317, 1.4188) X_447 = -HIRST INVERSE OF X(27) (0.8215, 0.9434) X_540 = DIRECTION OF VECTOR AX + BX + CX, where X = X(58) (0.9208, 0.6443) A B C X2 X58 X30 X511 X340 X447 X540 (a, b, c) = (5, 6, 7) | AB = 1

X540 (DIRECTION OF VECTOR AX + BX + CX, where X = X58) 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 \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(a,b,c) = a/(b + c)\), \(y = x(b,c,a)\), \(z = x(c,a,b)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X540 lies on the line at infinity.

▸ Incident Central Lines4 lines

{2, 58}, {30, 511}, {340, 447}, {376, 3430}