X3172

X6-CEVA CONJUGATE OF X25

X3172 = crosssum of X2 and X253
< 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) { 25, 32 }: Central Line L(25, 32) { 6, 64 }: Central Line L(6, 64) { 3, 112 }: Central Line L(3, 112) { 31, 607 }: Central Line L(31, 607) { 19, 1104 }: Central Line L(19, 1104) { 20, 1249 }: Central Line L(20, 1249) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1104 = CROSSPOINT OF X(1) AND X(28) (0.6311, 0.3042) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_1249 = ISOGONAL CONJUGATE OF X(1073) (-0.9482, -15.9845) X_3172 = -CEVA CONJUGATE OF X(25) (0.5527, 1.7582) A B C X6 X25 X32 X64 X3 X112 X31 X607 X19 X1104 X20 X1249 X3172 (a, b, c) = (5, 6, 7) | AB = 1

X3172 (X6-CEVA CONJUGATE OF X25) 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 \(x : y : z\) = X6 and \(u : v : w\) = X25
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): \(0.173218472170\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines12 lines

{3, 112}, {6, 64}, {19, 1104}, {20, 1249}, {24, 1384}, {25, 32}, {31, 607}, {41, 3195}, {204, 3198}, {232, 3053}, {608, 1042}, {1907, 3087}

▸ Functional Relations5 relations