X2022

RADICAL TRACE OF GALLATLY AND BROCARD CIRCLES

< 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 A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2022 = RADICAL TRACE OF GALLATLY AND BROCARD CIRCLES (0.3296, -0.1794) A B C X3 X6 X2022 (a, b, c) = (5, 6, 7) | AB = 1

X2022 (RADICAL TRACE OF GALLATLY AND BROCARD CIRCLES) 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) =, cos 5ω sin A + 3 sin(A - 3ω) + (cos A)(8 sin ω + sin 5ω)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.983394138213\)
▸ Incident Central Lines1 line

{3, 6}