X1406

X46-BETH CONJUGATE OF X46

X1406 = X34-Ceva conjugate of X56
< 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) { 31, 56 }: Central Line L(31, 56) { 65, 222 }: Central Line L(65, 222) { 55, 1066 }: Central Line L(55, 1066) { 57, 1203 }: Central Line L(57, 1203) { 3, 1464 }: Central Line L(3, 1464) { 1411, 1413 }: Central Line L(1411, 1413) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1066 = HASTINGS POINT (0.5873, 0.2963) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1203 = 3rd SARAGOSSA POINT OF X(58) (0.6034, 0.2712) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1464 = -BETH CONJUGATE OF X(758) (0.8584, 0.9843) X_1411 = -BETH CONJUGATE OF X(80) (1.0110, -0.2153) X_1413 = -BETH CONJUGATE OF X(84) (0.6037, 0.6378) X_1406 = -BETH CONJUGATE OF X(46) (0.6653, 0.5088) A B C X46 X31 X56 X65 X222 X55 X1066 X57 X1203 X3 X1464 X1411 X1413 X1406 (a, b, c) = (5, 6, 7) | AB = 1

X1406 (X46-BETH CONJUGATE OF X46) 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 \(u : v : w\) = X46
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.058995786709\)
▸ Incident Central Lines7 lines

{3, 1464}, {31, 56}, {55, 1066}, {57, 1203}, {65, 222}, {1411, 1413}, {1427, 1454}

▸ Functional Relations3 relations