X3284

INTERSECTION OF LINES X2X_340 AND X3X_6

Let L denote the line through X4 perpendicular to the Euler line. Coefficients for a trilinear equation for L are the trilinears for X3284.
< 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) { 401, 648 }: Central Line L(401, 648) { 3, 6 }: Brocard Axis { 23, 232 }: Central Line L(23, 232) { 2, 340 }: Central Line L(2, 340) { 441, 425 }: Euler Line A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_401 = BAILEY POINT (-0.0758, -1.4044) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_2 = CENTROID (0.5374, 0.2000) X_340 = ISOTOMIC CONJUGATE OF X(265) (1.2317, 1.4188) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_425 = -HIRST INVERSE OF X(21) (0.8561, 1.0339) X_3284 = INTERSECTION OF LINES X(2)X(340) AND X(3)X(6) (0.1903, -0.4095) A B C X401 X648 X3 X6 X23 X232 X2 X340 X441 X425 X3284 (a, b, c) = (5, 6, 7) | AB = 1

X3284 (INTERSECTION OF LINES X2X_340 AND X3X_6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(b^{2} + c^{2} - a^{2})[(b^{2} - c^{2})^{2} + a^{2}(b^{2} + c^{2} - 2a^{2})] : :\)
Search Value (6, 9, 13): \(1.360557864509\)
▸ Alternate Coordinates2 forms

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

  • Trilinears: \((\sin 2A) (3 \cos A - 2 \sin B \sin C) : :\)

▸ Incident Central Lines11 lines

{2, 340}, {3, 6}, {23, 232}, {30, 1990}, {112, 2693}, {231, 2072}, {248, 895}, {393, 3146}, {401, 648}, {441, 425}, {520, 647}

▸ Functional Relations15 relations