X3209

X56-CEVA CONJUGATE OF X25

X3209 = crosspoint of X19 and X2331
< 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) { 19, 56 }: Central Line L(19, 56) { 108, 281 }: Central Line L(108, 281) { 198, 208 }: Central Line L(198, 208) { 196, 347 }: Central Line L(196, 347) { 25, 1096 }: Central Line L(25, 1096) { 604, 608 }: Central Line L(604, 608) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_19 = CLAWSON POINT (0.6246, 0.4244) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_1096 = TRILINEAR SQUARE OF X(19) (0.6263, 0.5385) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_3209 = -CEVA CONJUGATE OF X(25) (0.6943, -0.3824) A B C X56 X25 X19 X108 X281 X198 X208 X196 X347 X1096 X604 X608 X3209 (a, b, c) = (5, 6, 7) | AB = 1

X3209 (X56-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 \(x : y : z\) = X56 and \(u : v : w\) = X25
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.065062763254\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines9 lines

{19, 56}, {25, 1096}, {108, 281}, {196, 347}, {198, 208}, {604, 608}, {607, 1400}, {1593, 2285}, {2187, 3195}

▸ Functional Relations3 relations