X3852

X732com(2nd EULER TRIANGLE)

< 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) { 32, 206 }: Central Line L(32, 206) { 66, 315 }: Central Line L(66, 315) { 30, 511 }: Central Line L(30, 511) { 6, 695 }: Central Line L(6, 695) { 141, 3491 }: Central Line L(141, 3491) { 159, 3499 }: Central Line L(159, 3499) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_3491 = INTERSECTION OF LINES X(1)X(295) AND X(4)X(69) (0.5262, 0.2536) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_3499 = INTERSECTION OF LINES X(3)X(695) AND X(6)X(76) (0.6625, 0.3232) X_3852 = com(2nd EULER TRIANGLE) (0.4059, -0.3720) A B C X32 X206 X66 X315 X30 X511 X6 X695 X141 X3491 X159 X3499 X3852 (a, b, c) = (5, 6, 7) | AB = 1

X3852 (X732com(2nd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{4}(b^{8} + c^{8} - a^{4}b^{4} - a^{4}c^{4})\)
▸ Incident Central Lines6 lines

{6, 695}, {30, 511}, {32, 206}, {66, 315}, {141, 3491}, {159, 3499}