X541

DIRECTION OF VECTOR AX + BX + CX, where X = X74

X541 = isogonal conjugate of X841
< 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, 74 }: Central Line L(2, 74) { 110, 376 }: Central Line L(110, 376) { 125, 381 }: Central Line L(125, 381) { 30, 511 }: Central Line L(30, 511) { 394, 399 }: Central Line L(394, 399) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_841 = ISOGONAL CONJUGATE OF X(541) (0.0813, -0.1897) X_2 = CENTROID (0.5374, 0.2000) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_399 = PARRY REFLECTION POINT (0.0032, 0.9936) X_541 = DIRECTION OF VECTOR AX + BX + CX, where X = X(74) (0.7497, -0.3472) A B C X841 X2 X74 X110 X376 X125 X381 X30 X511 X394 X399 X541 (a, b, c) = (5, 6, 7) | AB = 1

X541 (DIRECTION OF VECTOR AX + BX + CX, where X = X74) 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 \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(A,B,C) = 1/(\cos A - 2 \cos B \cos C)\), \(y = x(B,C,A)\), \(z = x(C,A,B)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X541 lies on the line at infinity.

▸ Incident Central Lines8 lines

{2, 74}, {30, 511}, {110, 376}, {125, 381}, {265, 3426}, {394, 399}, {3028, 3058}, {3448, 3543}

▸ Functional Relations1 relation