X529

DIRECTION OF VECTOR AX + BX + CX, where X = X12

X529 = isogonal conjugate of X38882
< 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, 12 }: Central Line L(2, 12) { 30, 511 }: Central Line L(30, 511) { 495, 993 }: Central Line L(495, 993) { 484, 1145 }: Central Line L(484, 1145) { 46, 1706 }: Central Line L(46, 1706) { 1001, 1056 }: Central Line L(1001, 1056) 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_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_495 = JOHNSON MIDPOINT (0.5666, 0.2382) X_993 = MIDPOINT OF X(1) AND X(63) (0.5140, 0.1578) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_1145 = 3rd EHRMANN POINT (0.3061, 0.2999) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_1706 = EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE) (0.5323, 0.2107) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_1056 = POINT ALCYONE (0.5756, 0.2499) X_529 = DIRECTION OF VECTOR AX + BX + CX, where X = X(12) (0.8589, 0.6909) A B C X2 X12 X30 X511 X495 X993 X484 X1145 X46 X1706 X1001 X1056 X529 (a, b, c) = (5, 6, 7) | AB = 1

X529 (DIRECTION OF VECTOR AX + BX + CX, where X = X12) 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 \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(A,B,C) = 1 + \cos(B-C)\), \(y = x(B,C,A)\), \(z = x(C,A,B)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X529 lies on the line at infinity.

▸ Incident Central Lines17 lines

{2, 12}, {8, 3474}, {30, 511}, {36, 3035}, {46, 1706}, {329, 3476}, {428, 1828}, {484, 1145}, {495, 993}, {908, 1319}, {956, 1478}, {1001, 1056}, {1146, 3509}, {1376, 3421}, {2098, 3058}, {2478, 3304}, {3036, 3218}

▸ Functional Relations1 relation

  • X529 = isogonal conjugate of X38882