X3173

X7-CEVA CONJUGATE OF X3

X3173 = cevapoint of X3157 and X3211
< 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, 90 }: Central Line L(1, 90) { 63, 77 }: Central Line L(63, 77) { 6, 226 }: Central Line L(6, 226) { 278, 651 }: Central Line L(278, 651) { 55, 916 }: Central Line L(55, 916) { 221, 758 }: Central Line L(221, 758) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1 = INCENTER (0.5714, 0.2333) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_916 = -CEVA CONJUGATE OF X(3) (0.0224, -0.0814) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_3173 = -CEVA CONJUGATE OF X(3) (0.8859, 0.3761) A B C X7 X3 X1 X90 X63 X77 X6 X226 X278 X651 X55 X916 X221 X758 X3173 (a, b, c) = (5, 6, 7) | AB = 1

X3173 (X7-CEVA CONJUGATE OF X3) 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 \(x : y : z\) = X7 and \(u : v : w\) = X3
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): \(1.032034782219\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines15 lines

{1, 90}, {3, 1794}, {6, 226}, {7, 2982}, {55, 916}, {63, 77}, {109, 3190}, {221, 758}, {223, 2323}, {278, 651}, {515, 1498}, {1362, 1397}, {1708, 2911}, {1936, 2947}, {2192, 2801}

▸ Functional Relations2 relations