X537

DIRECTION OF VECTOR AX + BX + CX, where X = X38

X537 = X513-Hirst inverse of X519
< 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, 38 }: Central Line L(2, 38) { 1, 190 }: Central Line L(1, 190) { 30, 511 }: Central Line L(30, 511) { 37, 551 }: Central Line L(37, 551) { 75, 668 }: Central Line L(75, 668) { 10, 1086 }: Central Line L(10, 1086) 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_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_1 = INCENTER (0.5714, 0.2333) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_537 = DIRECTION OF VECTOR AX + BX + CX, where X = X(38) (-0.0190, 0.3866) A B C X2 X38 X1 X190 X30 X511 X37 X551 X75 X668 X10 X1086 X537 (a, b, c) = (5, 6, 7) | AB = 1

X537 (DIRECTION OF VECTOR AX + BX + CX, where X = X38) 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 \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(a,b,c) = b^{2} + c^{2}\), \(y = x(b,c,a)\), \(z = x(c,a,b)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X537 lies on the line at infinity.

▸ Incident Central Lines7 lines

{1, 190}, {2, 38}, {10, 1086}, {30, 511}, {37, 551}, {75, 668}, {192, 3241}

▸ Functional Relations4 relations