X2011

INSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE)

X2011 is the insimilicenter(gallatly circle, Brocard circle).
< 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 { 1348, 2010 }: Central Line L(1348, 2010) { 1349, 2009 }: Central Line L(1349, 2009) 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_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5517, 0.2023) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.9341, -0.0718) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5463, 0.1455) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5673, 0.2394) X_2011 = INSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE) (0.5580, 0.1978) A B C X3 X6 X1348 X2010 X1349 X2009 X2011 (a, b, c) = (5, 6, 7) | AB = 1

X2011 (INSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE)) 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 \(f(A,B,C) = \cos(A - \omega ) + e \sin(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.572847126959\)
▸ Incident Central Lines3 lines

{3, 6}, {1348, 2010}, {1349, 2009}