X1393

X5-BETH CONJUGATE OF X5

X1393 = crosspoint of X57 and X273
< 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) { 12, 38 }: Central Line L(12, 38) { 28, 34 }: Central Line L(28, 34) { 2, 201 }: Central Line L(2, 201) { 56, 244 }: Central Line L(56, 244) { 227, 354 }: Central Line L(227, 354) { 46, 602 }: Central Line L(46, 602) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_2 = CENTROID (0.5374, 0.2000) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_227 = -CEVA CONJUGATE OF X(65) (0.4792, -0.0460) X_354 = WEILL POINT (0.5823, 0.2533) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_1393 = -BETH CONJUGATE OF X(5) (0.6196, 0.3615) A B C X5 X12 X38 X28 X34 X2 X201 X56 X244 X227 X354 X46 X602 X1393 (a, b, c) = (5, 6, 7) | AB = 1

X1393 (X5-BETH CONJUGATE OF X5) 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 \(u : v : w\) = X5
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.032347050375\)
▸ Incident Central Lines15 lines

{1, 1389}, {2, 201}, {11, 774}, {12, 38}, {28, 34}, {31, 1454}, {46, 602}, {56, 244}, {65, 1193}, {73, 942}, {225, 1210}, {227, 354}, {278, 1148}, {388, 982}, {595, 1421}

▸ Functional Relations2 relations