X2026

1st BROCARD-AXIS-GALLATLY-CIRCLE INTERSECTION

Of the two points of intersection of the Brocard axis, X3X6 with the Gallatly circle, X2026 is the one nearer to X3.
< 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) { 2027, 39 }: Brocard Axis { 3, 6 }: Brocard Axis { 2009, 2040 }: Central Line L(2009, 2040) { 2010, 2039 }: Central Line L(2010, 2039) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2027 = 2nd BROCARD-AXIS-GALLATLY-CIRCLE INTERSECTION (0.7024, 0.4363) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5673, 0.2394) X_2040 = = 2nd NINE-POINT-CIRCLE-KIEPERT-ASYMPTOTES INTERSECTION (0.6883, 0.4672) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.9341, -0.0718) X_2039 = 1st NINE-POINT-CIRCLE-KIEPERT-ASYMPTOTES INTERSECTION (0.4240, 0.0306) X_2026 = 1st BROCARD-AXIS-GALLATLY-CIRCLE INTERSECTION (0.4532, 0.0248) A B C X2027 X39 X3 X6 X2009 X2040 X2010 X2039 X2026 (a, b, c) = (5, 6, 7) | AB = 1

X2026 (1st BROCARD-AXIS-GALLATLY-CIRCLE INTERSECTION) 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 \(f(A,B,C) = e \sin(A + \omega ) + \cos(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.784569510886\)
▸ Incident Central Lines3 lines

{3, 6}, {2009, 2040}, {2010, 2039}

▸ Functional Relations1 relation