X906

INTERSECTION OF LINES X100X_112 AND X101X_109

X906 = X92-isoconjugate of X513
< 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) { 101, 109 }: Central Line L(101, 109) { 100, 112 }: Central Line L(100, 112) { 32, 218 }: Central Line L(32, 218) { 72, 248 }: Central Line L(72, 248) { 41, 601 }: Central Line L(41, 601) { 219, 577 }: Central Line L(219, 577) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_906 = INTERSECTION OF LINES X(100)X(112) AND X(101)X(109) (-0.2109, 0.3287) A B C X101 X109 X100 X112 X32 X218 X72 X248 X41 X601 X219 X577 X906 (a, b, c) = (5, 6, 7) | AB = 1

X906 (INTERSECTION OF LINES X100X_112 AND X101X_109) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: (cos A)/[\(wb^{2}\) - \(vc^{2}\) + a(wb - vc)],\(u : v : w\) = X3
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{3}(b^{2} + c^{2} - a^{2})/(b - c)\)
Search Value (6, 9, 13): \(-2.311286980824\)
▸ Alternate Coordinates1 form

  • Trilinears: \((\sin 2A)/(b - c) : :\)

▸ Incident Central Lines8 lines

{32, 218}, {41, 601}, {72, 248}, {100, 112}, {101, 109}, {163, 692}, {219, 577}, {1331, 4574}

▸ Functional Relations6 relations