X₁₁₂₁

X₇-BLAIKIE TRANSFORM OF X₂

For the definition of Blaikie transform, see X₉₀₃.

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

X₁₁₂₁ (X₇-BLAIKIE TRANSFORM OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 190}, {99, 333}

• Related Centers: X₁₀₅₅ (POINT ALIOTH), X₈ (NAGEL POINT), X₁₉₀ (YFF PARABOLIC POINT), X₉₉ (STEINER POINT), X₃₃₃ (CEVAPOINT OF X₈ AND X₉)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc/[(b + c - a)a - (a + b - c)(a + c - b)]\)

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

Search Value (6, 9, 13): \(4.525122731449\)

X₁₁₂₁ lies on the Steiner circumellipse.

▸ Incident Central Lines7 lines

{2, 664}, {8, 190}, {29, 648}, {99, 333}, {312, 668}, {519, 666}, {903, 918}

▸ Functional Relations10 relations

• X₁₁₂₁ = reflection of X_i in X_j for these (i,j): (2, 1146), (664, 2)

• X₁₁₂₁ = isogonal conjugate of X₁₀₅₅

• X₁₁₂₁ = isotomic conjugate of X₅₂₇

• X₁₁₂₁ = polar conjugate of X₂₃₇₁₀

• X₁₁₂₁ = complement of X₃₉₃₅₇

• X₁₁₂₁ = anticomplement of X₃₅₁₁₀

• X₁₁₂₁ = Steiner-circumellipse-antipode of X₆₆₄

• X₁₁₂₁ = projection from Steiner inellipse to Steiner circumellipse of X₁₁₄₆

• X₁₁₂₁ = antipode of X₈ in hyperbola {{A, B, C,X₂,X₈}}

• X₁₁₂₁ = trilinear pole of line X₂X₅₂₂