X1399

X35-BETH CONJUGATE OF X35

< 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) { 3, 47 }: Central Line L(3, 47) { 31, 56 }: Central Line L(31, 56) { 58, 65 }: Central Line L(58, 65) { 12, 171 }: Central Line L(12, 171) { 55, 255 }: Central Line L(55, 255) { 35, 500 }: Central Line L(35, 500) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_500 = ORTHOCENTER OF THE INCENTRAL TRIANGLE (0.5577, 0.1973) X_1399 = -BETH CONJUGATE OF X(35) (0.6178, 0.2762) A B C X35 X3 X47 X31 X56 X58 X65 X12 X171 X55 X255 X500 X1399 (a, b, c) = (5, 6, 7) | AB = 1

X1399 (X35-BETH CONJUGATE OF X35) 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 \(u : v : w\) = X35
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.647772849135\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \cos A - \cos 2A\)

▸ Incident Central Lines15 lines

{3, 47}, {6, 1195}, {12, 171}, {31, 56}, {34, 1454}, {35, 500}, {55, 255}, {58, 65}, {201, 896}, {213, 1415}, {580, 1155}, {595, 1319}, {920, 1060}, {1333, 1409}, {1402, 1408}