X532

DIRECTION OF VECTOR AX + BX + CX, where X = X17

X532 = isogonal conjugate of X2380
< 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, 17 }: Central Line L(2, 17) { 13, 298 }: Central Line L(13, 298) { 16, 299 }: Central Line L(16, 299) { 30, 511 }: Central Line L(30, 511) { 15, 616 }: Central Line L(15, 616) { 14, 622 }: Central Line L(14, 622) 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_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_616 = ANTICOMPLEMENT OF X(13) (0.4364, 0.0360) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_622 = ANTICOMPLEMENT OF X(16) (-2.0784, -4.0479) X_532 = DIRECTION OF VECTOR AX + BX + CX, where X = X(17) (0.8927, 0.6671) A B C X2 X17 X13 X298 X16 X299 X30 X511 X15 X616 X14 X622 X532 (a, b, c) = (5, 6, 7) | AB = 1

X532 (DIRECTION OF VECTOR AX + BX + CX, where X = X17) 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 \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(A,B,C) = \csc(A + \pi /6)\), \(y = x(B,C,A)\), \(z = x(C,A,B)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X532 lies on the line at infinity.

▸ Incident Central Lines9 lines

{2, 17}, {13, 298}, {14, 622}, {15, 616}, {16, 299}, {30, 511}, {395, 624}, {396, 618}, {397, 635}

▸ Functional Relations1 relation