X₂₄₈₁

INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE)

X₂₄₈₁ = Steiner-circumellipse-X₁-antipode of X₆₆₄

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

X₂₄₈₁ (INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 76}, {9, 75}

• Related Centers: X₂₂₂₃ (-ISOCONJUGATE OF X₆₇₃), X₈ (NAGEL POINT), X₇₆ (3rd BROCARD POINT), X₉ (MITTENPUNKT), X₇₅ (ISOTOMIC CONJUGATE OF INCENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = b^{2}c^{2}/(b^{2} + c^{2} - ab - ac)\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(3.015906883174\)

▸ Incident Central Lines17 lines

{1, 85}, {4, 150}, {8, 76}, {9, 75}, {21, 99}, {104, 927}, {239, 294}, {273, 1041}, {286, 648}, {314, 670}, {334, 350}, {767, 919}, {870, 1438}, {987, 1416}, {1441, 2346}, {1447, 2223}, {1462, 2298}

▸ Functional Relations14 relations

• X₂₄₈₁ = isogonal conjugate of X₂₂₂₃

• X₂₄₈₁ = isotomic conjugate of X₅₁₈

• X₂₄₈₁ = complement of X₃₉₃₅₀

• X₂₄₈₁ = X₁₉-isoconjugate of X₂₀₇₅₂

• X₂₄₈₁ = Steiner-circumellipse-X₁-antipode of X₆₆₄

• X₂₄₈₁ = Steiner-circumellipse-X₄-antipode of X₁₈₀₂₆

• X₂₄₈₁ = cevapoint of X_i and X_j these (i,j): (2,518), (11,918), (75,350), (105,1814)

• X₂₄₈₁ = X_i-cross conjugate of X_j for these (i,j): (239, 274), (518, 2), (885, 666)

• X₂₄₈₁ = crosssum of X₅₅ and X₂₁₁

• X₂₄₈₁ = trilinear pole of line X₂X₆₅₀

• X₂₄₈₁ = pole wrt polar circle of trilinear polar of X₅₀₈₉

• X₂₄₈₁ = X₄₈-isoconjugate (polar conjugate) of X₅₀₈₉

• X₂₄₈₁ = crossdifference of PU(97)

• X₂₄₈₁ = areal center of cevian triangles of PU(47)