X₃₉₃₄

X₂₀₂₃com(1st BROCARD TRIANGLE)

X₃₉₃₄ = centroid of ABCX₇₆

5, 6, 7 3, 4, 5 Kepler Kimberling

X₃₉₃₄ (X₂₀₂₃com(1st BROCARD TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 39}, {5, 141}

• Related Centers: X₂ (CENTROID), X₃₉ (BROCARD MIDPOINT), X₅ (NINE-POINT CENTER), X₁₄₁ (COMPLEMENT OF SYMMEDIAN POINT)

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 2b^{2}c^{2} + c^{2}a^{2} + a^{2}b^{2}\)

Search Value (6, 9, 13): \(3.161813365502\)

▸ Linear Combinations1 combination

• X₃₉₃₄ = \(3\) X₂ + X₇₆

▸ Incident Central Lines26 lines

{2, 39}, {3, 3734}, {5, 141}, {32, 183}, {69, 2548}, {75, 1574}, {83, 385}, {140, 620}, {187, 384}, {230, 736}, {232, 1235}, {262, 3090}, {264, 3199}, {316, 2896}, {325, 1506}, {350, 1500}, {574, 1975}, {726, 3634}, {730, 1125}, {732, 3589}, {1015, 1909}, {1207, 3499}, {1656, 3095}, {2275, 3761}, {2276, 3760}, {3094, 3763}

▸ Functional Relations7 relations

• X₃₉₃₄ = isotomic conjugate of isogonal conjugate of X₂₀₉₆₅

• X₃₉₃₄ = polar conjugate of isogonal conjugate of X₂₂₀₆₂

• X₃₉₃₄ = centroid of ABCX₇₆

• X₃₉₃₄ = Kosnita(X₇₆,X₂)

• X₃₉₃₄ = complement of X₃₉

• X₃₉₃₄ = X₂₀₂₃-of-1st-Brocard-triangle

• X₃₉₃₄ = perspector of the medial triangle and the tangential triangle, wrt the medial triangle, of the bicevian conic of X₂ and X₆