X533

DIRECTION OF VECTOR AX + BX + CX, where X = X18

X533 = isogonal conjugate of X2381
< 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, 18 }: Central Line L(2, 18) { 14, 299 }: Central Line L(14, 299) { 15, 298 }: Central Line L(15, 298) { 30, 511 }: Central Line L(30, 511) { 16, 617 }: Central Line L(16, 617) { 13, 621 }: Central Line L(13, 621) 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_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_617 = ANTICOMPLEMENT OF X(14) (-0.2146, 0.8285) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_621 = ANTICOMPLEMENT OF X(15) (0.5084, 0.2242) X_533 = DIRECTION OF VECTOR AX + BX + CX, where X = X(18) (0.0625, -0.1448) A B C X2 X18 X14 X299 X15 X298 X30 X511 X16 X617 X13 X621 X533 (a, b, c) = (5, 6, 7) | AB = 1

X533 (DIRECTION OF VECTOR AX + BX + CX, where X = X18) 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: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X533 lies on the line at infinity.

▸ Incident Central Lines9 lines

{2, 18}, {13, 621}, {14, 299}, {15, 298}, {16, 617}, {30, 511}, {395, 619}, {396, 623}, {398, 636}

▸ Functional Relations1 relation