X1408

X58-BETH CONJUGATE OF X58

X1408 = X1412-Ceva conjugate of X1333
< 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) { 56, 58 }: Central Line L(56, 58) { 65, 81 }: Central Line L(65, 81) { 60, 757 }: Central Line L(60, 757) { 603, 604 }: Central Line L(603, 604) { 283, 1037 }: Central Line L(283, 1037) { 21, 1319 }: Central Line L(21, 1319) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_757 = ISOGONAL CONJUGATE OF X(756) (0.5971, 0.2688) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_1408 = -BETH CONJUGATE OF X(58) (0.6479, 0.3898) A B C X58 X56 X65 X81 X60 X757 X603 X604 X283 X1037 X21 X1319 X1408 (a, b, c) = (5, 6, 7) | AB = 1

X1408 (X58-BETH CONJUGATE OF X58) 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 \(u : v : w\) = X58
Search Value (6, 9, 13): \(0.062309364089\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{2}/((b + c) (a - b - c)) : :\)

▸ Incident Central Lines10 lines

{21, 1319}, {56, 58}, {60, 757}, {65, 81}, {283, 1037}, {284, 1466}, {603, 604}, {1398, 1407}, {1399, 1402}, {1413, 1474}

▸ Functional Relations5 relations