X538

DIRECTION OF VECTOR AX + BX + CX, where X = X39

X538 = isogonal conjugate of X729
< 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, 39 }: Central Line L(2, 39) { 99, 187 }: Central Line L(99, 187) { 115, 325 }: Central Line L(115, 325) { 148, 316 }: Central Line L(148, 316) { 30, 511 }: Central Line L(30, 511) { 183, 574 }: Central Line L(183, 574) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_729 = EVEN (- 2, 0) CIRCUMCIRCLE POINT (1.0096, 0.1290) X_2 = CENTROID (0.5374, 0.2000) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_99 = STEINER POINT (0.1109, 0.4322) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3904, -0.2646) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_538 = DIRECTION OF VECTOR AX + BX + CX, where X = X(39) (1.0053, 0.5542) A B C X729 X2 X39 X99 X187 X115 X325 X148 X316 X30 X511 X183 X574 X538 (a, b, c) = (5, 6, 7) | AB = 1

X538 (DIRECTION OF VECTOR AX + BX + CX, where X = X39) 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 \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(a,b,c) = a(b^{2} + c^{2})\), \(y = x(b,c,a)\), \(z = x(c,a,b)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X538 lies on the line at infinity.

▸ Incident Central Lines21 lines

{2, 39}, {30, 511}, {32, 1003}, {69, 2549}, {75, 1573}, {99, 187}, {115, 325}, {148, 316}, {183, 574}, {230, 620}, {262, 3545}, {350, 1015}, {381, 3095}, {591, 3102}, {599, 3094}, {671, 1916}, {886, 3228}, {1316, 3292}, {1500, 1909}, {1569, 2021}, {1991, 3103}

▸ Functional Relations5 relations