X992

INTERSECTION OF LINES X2X_6 AND X9X_39

< 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) { 2, 6 }: Centroid–Symmedian Line { 9, 39 }: Central Line L(9, 39) { 44, 583 }: Central Line L(44, 583) { 238, 1009 }: Central Line L(238, 1009) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_9 = MITTENPUNKT (0.5110, 0.1615) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_1009 = INTERCEPT OF EULER LINE AND LINE X(1)X(39) (0.5532, 0.2412) X_992 = INTERSECTION OF LINES X(2)X(6) AND X(9)X(39) (0.2678, -0.0897) A B C X2 X6 X9 X39 X44 X583 X238 X1009 X992 (a, b, c) = (5, 6, 7) | AB = 1

X992 (INTERSECTION OF LINES X2X_6 AND X9X_39) 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 \(f(a,b,c) = a^{3}(b + c) + a^{2}(b^{2} + c^{2}) - abc(b + c) - bc(b + c)^{2}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(47.057524952315\)
▸ Incident Central Lines4 lines

{2, 6}, {9, 39}, {44, 583}, {238, 1009}