X1451

X405-BETH CONJUGATE OF X405

< 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) { 6, 41 }: Central Line L(6, 41) { 28, 34 }: Central Line L(28, 34) { 31, 65 }: Central Line L(31, 65) { 1, 201 }: Central Line L(1, 201) { 270, 273 }: Central Line L(270, 273) { 36, 581 }: Central Line L(36, 581) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) 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_31 = 2nd POWER POINT (0.6228, 0.3008) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1 = INCENTER (0.5714, 0.2333) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_581 = ORTHOHARMONIC OF X(284) (0.5657, 0.2106) X_1451 = -BETH CONJUGATE OF X(405) (0.6121, 0.2965) A B C X405 X6 X41 X28 X34 X31 X65 X1 X201 X270 X273 X36 X581 X1451 (a, b, c) = (5, 6, 7) | AB = 1

X1451 (X405-BETH CONJUGATE OF X405) 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 \(u : v : w\) = X405
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.533965260888\)
▸ Incident Central Lines10 lines

{1, 201}, {6, 41}, {28, 34}, {31, 65}, {36, 581}, {46, 601}, {255, 942}, {270, 273}, {1038, 1445}, {1106, 1427}