X3178

X12-CEVA CONJUGATE OF X10

X3178 = X12-Ceva conjugate of X10
< 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) { 1, 2 }: Nagel Line A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_3178 = -CEVA CONJUGATE OF X(10) (0.6269, 0.2877) A B C X12 X10 X1 X2 X3178 (a, b, c) = (5, 6, 7) | AB = 1

X3178 (X12-CEVA CONJUGATE OF X10) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X12 and \(u : v : w\) = X10
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-0.541604760106\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines1 line

{1, 2}

▸ Functional Relations1 relation