X3415

X1-VERTEX CONJUGATE OF X2

X3415 = isogonal conjugate of X3416
< 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) { 22, 55 }: Central Line L(22, 55) { 41, 386 }: Central Line L(41, 386) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3416 = ISOGONAL CONJUGATE OF X(3415) (0.4408, 0.0994) X_22 = EXETER POINT (0.4143, -0.1221) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_3415 = -VERTEX CONJUGATE OF X(2) (0.6348, 0.3922) A B C X3416 X22 X55 X41 X386 X3415 (a, b, c) = (5, 6, 7) | AB = 1

X3415 (X1-VERTEX CONJUGATE OF X2) 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 \(x : y : z\) = X2
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.153567572406\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines2 lines

{22, 55}, {41, 386}

▸ Functional Relations2 relations