X3286

INTERSECTION OF LINES X3X_6 AND X7X_21

Let L denote the line through X37 perpendicular to the Euler line. Coefficients for a trilinear equation for L are the trilinears for X3286.
< 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) circumcircle: Circumcircle of △ABC { 3, 3110 }: Brocard Axis { 3, 6 }: Brocard Axis { 7, 21 }: Central Line L(7, 21) { 55, 81 }: Central Line L(55, 81) { 36, 238 }: Central Line L(36, 238) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_3110 = ORTHOGONAL PROJECTION OF X(1) ON BROCARD AXIS (0.5773, 0.2297) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_7 = GERGONNE POINT (0.5903, 0.2769) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_3286 = INTERSECTION OF LINES X(3)X(6) AND X(7)X(21) (1.4038, 1.5947) A B C X3 X3110 X6 X7 X21 X55 X81 X36 X238 X3286 (a, b, c) = (5, 6, 7) | AB = 1

X3286 (INTERSECTION OF LINES X3X_6 AND X7X_21) 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 \(f(a,b,c) = a(b^{2} + c^{2} - ab - ac)/(b + c)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.816622493957\)
▸ Incident Central Lines19 lines

{3, 6}, {7, 21}, {28, 277}, {31, 2274}, {36, 238}, {55, 81}, {63, 2352}, {110, 840}, {141, 1009}, {198, 1778}, {241, 1876}, {283, 1037}, {333, 1376}, {518, 2223}, {672, 1818}, {741, 813}, {759, 1308}, {940, 1011}, {958, 1010}

▸ Functional Relations7 relations