X2029

2nd BROCARD-AXIS-MOSES-CIRCLE INTERSECTION

X2029 = isogonal conjugate of isotomic conjugate of X39022
< 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 { 115, 2040 }: Central Line L(115, 2040) { 1506, 2039 }: Central Line L(1506, 2039) 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_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_2040 = = 2nd NINE-POINT-CIRCLE-KIEPERT-ASYMPTOTES INTERSECTION (0.6883, 0.4672) X_1506 = INSIMILICENTER OF MOSES AND NINE-POINT CIRCLES (0.5676, 0.2392) X_2039 = 1st NINE-POINT-CIRCLE-KIEPERT-ASYMPTOTES INTERSECTION (0.4240, 0.0306) X_2029 = 2nd BROCARD-AXIS-MOSES-CIRCLE INTERSECTION (0.6952, 0.4245) A B C X3 X6 X115 X2040 X1506 X2039 X2029 (a, b, c) = (5, 6, 7) | AB = 1

X2029 (2nd BROCARD-AXIS-MOSES-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 \(f(A,B,C) = \sin A + e \sin(A + \omega ) - \sin(A + 2\omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.169342567051\)

X2029 lies on the Brocard inellipse.

▸ Incident Central Lines3 lines

{3, 6}, {115, 2040}, {1506, 2039}

▸ Functional Relations2 relations

  • X2029 = isogonal conjugate of isotomic conjugate of X39022

  • X2029 = crosssum of the vertices of the Steiner circumellipse