X198

X9-CEVA CONJUGATE OF X6

X198 = isogonal conjugate of X189
< 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) { 3, 9 }: Central Line L(3, 9) { 19, 25 }: Central Line L(19, 25) { 6, 41 }: Central Line L(6, 41) { 64, 71 }: Central Line L(64, 71) { 101, 102 }: Central Line L(101, 102) { 154, 212 }: Central Line L(154, 212) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) A B C X9 X6 X3 X19 X25 X41 X64 X71 X101 X102 X154 X212 X198 (a, b, c) = (5, 6, 7) | AB = 1

X198 (X9-CEVA CONJUGATE OF X6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = a(\cos B + \cos C - \cos A - 1)\)
Search Value (6, 9, 13): \(-13.649689379823\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(a (a^{3} + a^{2} (b + c) - a (b + c)^{2} - (b - c)^{2} (b + c)) : :\)

  • Trilinears: \(s \cos A - r \cot(A/2) : :\)

▸ Incident Central Lines13 lines

{3, 9}, {6, 41}, {19, 25}, {5, 1030}, {64, 71}, {100, 346}, {101, 102}, {154, 212}, {208, 227}, {218, 579}, {284, 859}, {478, 577}, {958, 966}

▸ Functional Relations9 relations