X1421

X149-BETH CONJUGATE OF X149

< 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) { 1, 5 }: Feuerbach Line { 31, 57 }: Central Line L(31, 57) { 34, 106 }: Central Line L(34, 106) { 595, 1393 }: Central Line L(595, 1393) { 1279, 1465 }: Central Line L(1279, 1465) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_1 = INCENTER (0.5714, 0.2333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_1393 = -BETH CONJUGATE OF X(5) (0.6196, 0.3615) X_1279 = MIDPOINT OF X(1) AND X(238) (1.0952, 0.8554) X_1465 = -BETH CONJUGATE OF X(908) (0.7719, 1.0314) X_1421 = -BETH CONJUGATE OF X(149) (1.7143, -0.9331) A B C X149 X1 X5 X31 X57 X34 X106 X595 X1393 X1279 X1465 X1421 (a, b, c) = (5, 6, 7) | AB = 1

X1421 (X149-BETH CONJUGATE OF X149) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X149
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.231368000903\)
▸ Incident Central Lines5 lines

{1, 5}, {31, 57}, {34, 106}, {595, 1393}, {1279, 1465}