X3418

X1-VERTEX CONJUGATE OF X7

X3418 = isogonal conjugate of X3419
< 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, 48 }: Central Line L(36, 48) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3419 = ISOGONAL CONJUGATE OF X(3418) (0.4918, 0.1745) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_3418 = -VERTEX CONJUGATE OF X(7) (0.6289, 0.2917) A B C X3419 X36 X48 X3418 (a, b, c) = (5, 6, 7) | AB = 1

X3418 (X1-VERTEX CONJUGATE OF X7) 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 \(u : v : w\) = X1 and \(x : y : z\) = X7
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.651387340280\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{2}/[a^{4} - a^{3}(b + c) + a(b + c)(b^{2} + c^{2}) - (b^{2} - c^{2})^{2}] (E\). Danneels)

▸ Incident Central Lines1 line

{36, 48}

▸ Functional Relations1 relation