X3177

X9-CEVA CONJUGATE OF X2

X3177 = reflection of X85 in X1212
< 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) { 85, 1212 }: Central Line L(85, 1212) { 2, 85 }: Central Line L(2, 85) { 63, 194 }: Central Line L(63, 194) { 144, 145 }: Central Line L(144, 145) { 105, 330 }: Central Line L(105, 330) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_1212 = ISOGONAL CONJUGATE OF X(1170) (0.5256, 0.1789) X_2 = CENTROID (0.5374, 0.2000) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_3177 = -CEVA CONJUGATE OF X(2) (0.4903, 0.1157) A B C X85 X1212 X2 X63 X194 X144 X145 X105 X330 X3177 (a, b, c) = (5, 6, 7) | AB = 1

X3177 (X9-CEVA CONJUGATE OF X2) 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 \(x : y : z\) = X9 and \(u : v : w\) = X2
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): \(5.148692764633\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines9 lines

{2, 85}, {63, 194}, {105, 330}, {144, 145}, {220, 664}, {329, 1655}, {672, 3212}, {894, 2263}, {1654, 3152}

▸ Functional Relations7 relations