X₁₂₇₉

MIDPOINT OF X₁ AND X₂₃₈

X₁₂₇₉ is the midpoint of X₁ and X₂₃₈.

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

X₁₂₇₉ (MIDPOINT OF X₁ AND X₂₃₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 238}

• Related Centers: X₁ (INCENTER), X₂₃₈ (-LINE CONJUGATE OF X₃₇)

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

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

Search Value (6, 9, 13): \(-1.005048302920\)

▸ Incident Central Lines13 lines

{1, 6}, {31, 354}, {55, 614}, {105, 910}, {145, 344}, {210, 748}, {244, 902}, {513, 663}, {516, 1086}, {551, 752}, {595, 942}, {56, 1418}, {1201, 2293}

▸ Functional Relations14 relations

• X₁₂₇₉ = midpoint of X₁ and X₂₃₈

• X₁₂₇₉ = reflection of X₄₄ in X₂₃₈

• X₁₂₇₉ = isogonal conjugate of X₁₂₈₀

• X₁₂₇₉ = complement of X₃₂₈₅₀

• X₁₂₇₉ = anticomplement of X₃₈₂₃

• X₁₂₇₉ = crosspoint of X_i and X_j for these (i,j): (1, 105), (927, 1016)

• X₁₂₇₉ = crosssum of X_i and X_j for these (i,j): (1, 518), (926, 1015)

• X₁₂₇₉ = crossdifference of every pair of points on line X₉X₅₁₃

• X₁₂₇₉ = {X₁,X₉}-harmonic conjugate of X₃₂₄₂

• X₁₂₇₉ = crossdifference of PU(56)

• X₁₂₇₉ = midpoint of PU(96)

• X₁₂₇₉ = bicentric sum of PU(96)

• X₁₂₇₉ = X₂-Ceva conjugate of X₃₉₀₄₈

• X₁₂₇₉ = perspector of hyperbola {{A, B, C,X₅₇,X₁₀₀}}

Notes

X₁₂₇₉ is the {X₁,X₁₀₀₁}-harmonic conjugate of X₃₇.