X3446

X513-VERTEX CONJUGATE OF X513

X3446 = isogonal conjugate of X149
< 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) { 36, 518 }: Central Line L(36, 518) { 840, 1618 }: Central Line L(840, 1618) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_840 = ISOGONAL CONJUGATE OF X(528) (0.0800, 0.3919) X_1618 = TCC-PERSPECTOR OF X(59) (0.0333, 0.7076) X_3446 = -VERTEX CONJUGATE OF X(513) (0.1111, 0.1814) A B C X692 X6 X36 X518 X840 X1618 X3446 (a, b, c) = (5, 6, 7) | AB = 1

X3446 (X513-VERTEX CONJUGATE OF X513) 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 \(f(a,b,c) = a/[a^{2}vwyz - ux(bw + cv)(bz + cy)]\), where \(u : v : w\) = X513 and \(x : y : z\) = X513
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-28.717631015447\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{2}/[a^{3} - a^{2}b - a^{2}c + a(b^{2} - bc + c^{2}) - (b + c)(b - c)^{2}] (E\). Danneels)

▸ Incident Central Lines2 lines

{36, 518}, {840, 1618}

▸ Functional Relations2 relations