X3866

PERSPECTOR OF ABC AND T(a², a² + b²)

X3866 is the perspector of ABC and t(a², a² + b²).
< 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) { 69, 194 }: Central Line L(69, 194) { 83, 419 }: Central Line L(83, 419) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_419 = -HIRST INVERSE OF X(25) (0.7266, 0.6950) X_3866 = PERSPECTOR OF ABC AND T(a2, a2 + b2) (0.5479, 0.1870) A B C X69 X194 X83 X419 X3866 (a, b, c) = (5, 6, 7) | AB = 1

X3866 (PERSPECTOR OF ABC AND T(a², a² + b²)) 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 \(f(a,b,c) = (b^{4} + a^{2}c^{2})(c^{4} + a^{2}b^{2})(3a^{2} + b^{2} + c^{2})\)
Search Value (6, 9, 13): \(2.381131345241\)
▸ Incident Central Lines2 lines

{69, 194}, {83, 419}