X527

DIRECTION OF VECTOR AX + BX + CX, where X = X7

X527 = isogonal conjugate of X2291
< 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, 7 }: Centroid–Gergonne Line { 190, 320 }: Central Line L(190, 320) { 30, 511 }: Central Line L(30, 511) { 44, 1086 }: Central Line L(44, 1086) { 72, 1242 }: Central Line L(72, 1242) { 666, 673 }: Central Line L(666, 673) 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_7 = GERGONNE POINT (0.5903, 0.2769) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1242 = ISOGONAL CONJUGATE OF X(1005) (0.6074, 0.3216) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_673 = TRILINEAR POLE OF LINE X(1)X(514) (0.9471, -0.0769) X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X(7) (0.8698, 0.6836) A B C X2 X7 X190 X320 X30 X511 X44 X1086 X72 X1242 X666 X673 X527 (a, b, c) = (5, 6, 7) | AB = 1

X527 (DIRECTION OF VECTOR AX + BX + CX, where X = X7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((2ax - by - cz)/a\), where \(x = x(a,b,c) = 1/[a(b + c - a)]\), \(y = x(b,c,a)\), \(z = x(c,a,b)\)
Barycentrics: \(2a^{2} - a(b + c) - (b - c)^{2} : :\)

X527 lies on the line at infinity.

▸ Incident Central Lines25 lines

{2, 7}, {30, 511}, {44, 1086}, {69, 2321}, {72, 1242}, {190, 320}, {200, 3474}, {239, 1266}, {269, 2324}, {347, 1419}, {376, 2096}, {381, 2095}, {390, 3241}, {551, 993}, {599, 2097}, {651, 2323}, {666, 673}, {896, 3011}, {1156, 3254}, {1478, 2093}, {1738, 1757}, {2340, 3000}, {2346, 3255}, {2551, 3339}, {2951, 3174}

▸ Functional Relations6 relations