X2674

ISOGONAL CONJUGATE OF X2672

X2674 is the isogonal conjugate of X2672.
< 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, 6 }: Brocard Axis { 2, 2671 }: Central Line L(2, 2671) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2672 = 2nd GOLDEN ARBELOS POINT (0.3508, 0.0923) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_2671 = 1st GOLDEN ARBELOS POINT (0.5720, 0.2475) X_2674 = ISOGONAL CONJUGATE OF X(2672) (0.6690, 0.3812) A B C X2672 X3 X6 X2 X2671 X2674 (a, b, c) = (5, 6, 7) | AB = 1

X2674 (ISOGONAL CONJUGATE OF X2672) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2 \cos A -τ^{2}\sin A : :\), where τ = (1 + \(\sqrt{5}\))/2 = golden ratio
Barycentrics: \((S+(\sqrt{5}-3) S_{A}) \cdot (S_{B}+S_{C})\) (C. Lozada, 7/13/19)
Search Value (6, 9, 13): \(-0.966232370821\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cos[A + arccot(3 - 5^{1/2})] : :\) (M. Iliev, 5/13/07)

▸ Incident Central Lines2 lines

{2, 2671}, {3, 6}

▸ Functional Relations3 relations

  • X2674 = isogonal conjugate of X2672

  • X2674 = inverse-in-Brocard-circle of X2673

  • X2674 = radical center of Lucas(-τ2) circles, where τ = (1 + \(\sqrt{5}\))/2 = golden ratio