X391

INTERSECTION OF LINES X(2,6) AND X(8,9)

X391 is the {X8,X9}-harmonic conjugate of X346.
< 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) { 8, 9 }: Central Line L(8, 9) { 2, 6 }: Centroid–Symmedian Line { 37, 145 }: Central Line L(37, 145) { 75, 144 }: Central Line L(75, 144) { 319, 344 }: Central Line L(319, 344) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_391 = INTERSECTION OF LINES X(2,6) AND X(8,9) (0.4857, 0.1443) A B C X346 X8 X9 X2 X6 X37 X145 X75 X144 X319 X344 X391 (a, b, c) = (5, 6, 7) | AB = 1

X391 (INTERSECTION OF LINES X(2,6) AND X(8,9)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(3a + b + c)(b + c - a) : :\)
Barycentrics: \((3a + b + c)(b + c - a) : :\)
Search Value (6, 9, 13): \(4.179129206605\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(a^{2} - s^{2} : b^{2} - s^{2} : c^{2} - s^{2}\)

▸ Incident Central Lines6 lines

{2, 6}, {8, 9}, {20, 573}, {37, 145}, {75, 144}, {319, 344}

▸ Functional Relations1 relation