X1457

X517-BETH CONJUGATE OF X517

X1457 = X106-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) { 1, 4 }: Incenter–Orthocenter Line { 31, 56 }: Central Line L(31, 56) { 36, 109 }: Central Line L(36, 109) { 48, 608 }: Central Line L(48, 608) { 3, 945 }: Central Line L(3, 945) { 57, 957 }: Central Line L(57, 957) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_945 = ISOGONAL CONJUGATE OF X(944) (0.6020, 0.4506) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_957 = ISOGONAL CONJUGATE OF X(956) (0.6245, 0.3599) X_1457 = -BETH CONJUGATE OF X(517) (0.7719, 1.0314) A B C X517 X1 X4 X31 X56 X36 X109 X48 X608 X3 X945 X57 X957 X1457 (a, b, c) = (5, 6, 7) | AB = 1

X1457 (X517-BETH CONJUGATE OF X517) 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 \(u : v : w\) = X517
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.226477095001\)
▸ Incident Central Lines16 lines

{1, 4}, {3, 945}, {31, 56}, {36, 109}, {48, 608}, {57, 957}, {65, 1193}, {201, 960}, {222, 999}, {350, 664}, {392, 1214}, {478, 604}, {513, 663}, {517, 1465}, {1055, 1415}, {1394, 1420}

▸ Functional Relations5 relations