X₂₂₉₁

X₂-ISOCONJUGATE OF X₁₁₅₅

X₂₂₉₁ = isogonal conjugate of X₅₂₇

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

X₂₂₉₁ (X₂-ISOCONJUGATE OF X₁₁₅₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {9, 100}, {6, 109}

• Related Centers: X₅₂₇ (DIRECTION OF VECTOR AX + BX + CX, where X = X), X₉ (MITTENPUNKT), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₆ (SYMMEDIAN POINT), X₁₀₉ (Ψ(INCENTER, CIRCUMCENTER))

Trilinears: \(a/(a (2 a - b - c) - (b - c)^{2}) : :\)

Search Value (6, 9, 13): \(6.134998942481\)

X₂₂₉₁ lies on the circumcircle.

▸ Incident Central Lines28 lines

{6, 109}, {9, 100}, {19, 108}, {55, 101}, {57, 934}, {99, 333}, {103, 654}, {105, 1024}, {106, 665}, {110, 284}, {112, 2299}, {165, 1292}, {573, 1293}, {649, 840}, {672, 901}, {673, 927}, {902, 919}, {909, 2272}, {910, 2161}, {932, 2319}, {1055, 2078}, {1108, 2160}, {1155, 1308}, {1174, 1200}, {1305, 1751}, {1310, 2339}, {1630, 2164}, {2280, 2364}

▸ Functional Relations9 relations

• X₂₂₉₁ = isogonal conjugate of X₅₂₇

• X₂₂₉₁ = anticomplement of X₃₁₈₄₄

• X₂₂₉₁ = circumcircle-antipode of X₂₈₂₉₁

• X₂₂₉₁ = cevapoint of X₆ and X₁₀₅₅

• X₂₂₉₁ = X₂₀₇₈-cross conjugate of X₁₁₇₄

• X₂₂₉₁ = trilinear pole of line X₆X₆₆₃

• X₂₂₉₁ = Ψ(X₁, X₆₅₀)

• X₂₂₉₁ = Ψ(X₆, X₆₆₃)

• X₂₂₉₁ = Ψ(X₁₉₀, X₈)