X1448

X377-BETH CONJUGATE OF X377

< 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, 7 }: Soddy Line { 28, 34 }: Central Line L(28, 34) { 65, 222 }: Central Line L(65, 222) { 46, 255 }: Central Line L(46, 255) { 223, 386 }: Central Line L(223, 386) { 241, 405 }: Central Line L(241, 405) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) 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_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_1448 = -BETH CONJUGATE OF X(377) (0.6169, 0.3386) A B C X377 X1 X7 X28 X34 X65 X222 X46 X255 X223 X386 X241 X405 X1448 (a, b, c) = (5, 6, 7) | AB = 1

X1448 (X377-BETH CONJUGATE OF X377) 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 \(u : v : w\) = X377
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.208745305998\)
▸ Incident Central Lines14 lines

{1, 7}, {3, 1427}, {28, 34}, {46, 255}, {65, 222}, {85, 1010}, {223, 386}, {226, 975}, {241, 405}, {443, 948}, {942, 1407}, {998, 1413}, {1104, 1418}, {1465, 1466}