X1990

ORTHIC-AXIS INTERCEPT OF LINE X4X_6

X1990 is described in section 6.4.2 of the downloadable article cited at X1989.
< 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) { 297, 648 }: Central Line L(297, 648) { 4, 6 }: Van Aubel Line { 50, 112 }: Central Line L(50, 112) { 140, 216 }: Central Line L(140, 216) { 230, 231 }: Central Line L(230, 231) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_50 = -CEVA CONJUGATE OF X(184) (2.1559, 2.8368) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_1990 = ORTHIC-AXIS INTERCEPT OF LINE X(4)X(6) (0.6502, 0.7938) A B C X297 X648 X4 X6 X50 X112 X140 X216 X230 X231 X1990 (a, b, c) = (5, 6, 7) | AB = 1

X1990 (ORTHIC-AXIS INTERCEPT OF LINE X4X_6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc[a^{2}(b^{2} + c^{2} - 2a^{2}) + (b^{2} - c^{2})^{2}]/(b^{2} + c^{2} - a^{2}) : :\)
Barycentrics: \([a^{2}(b^{2} + c^{2} - 2a^{2}) + (b^{2} - c^{2})^{2}]/(b^{2} + c^{2} - a^{2}) : :\)
Search Value (6, 9, 13): \(0.569371567391\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((\tan A)(\cos A - 2 \cos B \cos C) : :\)

  • Trilinears: \(\sin A - 2 \tan A \cos B \cos C : :\)

▸ Incident Central Lines13 lines

{4, 6}, {44, 1785}, {50, 112}, {140, 216}, {186, 1138}, {230, 231}, {297, 340}, {395, 471}, {396, 470}, {403, 1989}, {458, 597}, {550, 577}, {1033, 1609}

▸ Functional Relations12 relations