X2015

INSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL CIRCLE)

X2015 is the insimilicenter(gallatly circle, orthocentroidal 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) { 39, 381 }: Central Line L(39, 381) { 1344, 1689 }: Central Line L(1344, 1689) { 1345, 1690 }: Central Line L(1345, 1690) { 1346, 2010 }: Central Line L(1346, 2010) { 1347, 2009 }: Central Line L(1347, 2009) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_1344 = INSIMILICENTER(CIRCUMCIRCLE, ORTHOCENTROIDAL CIRCLE) (0.5621, 0.2645) X_1689 = INVERSE-IN-BROCARD-CIRCLE OF X(1687) (0.6471, 0.3451) X_1345 = EXSIMILICENTER(CIRCUMCIRCLE, ORTHOCENTROIDAL CIRCLE) (0.5942, 0.3485) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5529, 0.1894) X_1346 = INSIMILICENTER(NINE-POINT CIRCLE, ORTHOCENTROIDAL CIRCLE) (0.5694, 0.2836) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.9341, -0.0718) X_1347 = EXSIMILICENTER(NINE-POINT CIRCLE, ORTHOCENTROIDAL CIRCLE) (0.5879, 0.3320) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5673, 0.2394) X_2015 = INSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL CIRCLE) (0.5757, 0.2774) A B C X39 X381 X1344 X1689 X1345 X1690 X1346 X2010 X1347 X2009 X2015 (a, b, c) = (5, 6, 7) | AB = 1

X2015 (INSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL 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 \(f(a,b,c) = \cos A + 4 \cos B \cos C + J \sin(A + \omega )\), \(J = |OH|/R\); see X1113
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.557936044985\)
▸ Incident Central Lines5 lines

{39, 381}, {1344, 1689}, {1345, 1690}, {1346, 2010}, {1347, 2009}