X₉₂₅

ANTICOMPLEMENT OF X₁₃₆

X₉₂₅ is the anticomplement of X₁₃₆.

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

X₉₂₅ (ANTICOMPLEMENT OF X₁₃₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Anticomplementary Triangle △K_aK_bK_c — vertices K_a, K_b, K_c (Formed by lines through A, B, C parallel to opposite sides)

• Central Lines: {2, 136}

• Related Centers: X₂ (CENTROID), X₁₃₆ (INTERSECTION OF LINE X)

Trilinears: \((\sin A)/(\sec 2B - \sec 2C) : :\)

Barycentrics: \(1/((b^{2} - c^{2}) (a^{4} + b^{4} + c^{4} - 2 a^{2} b^{2} - 2 a^{2} c^{2})) : :\)

Search Value (6, 9, 13): \(-0.551104905747\)

▸ Alternate Coordinates1 form

• Trilinears: \(1/(b \cos(A - B) - c \cos(A - C)) : :\)

X₉₂₅ lies on the circumcircle.

▸ Incident Central Lines10 lines

{2, 136}, {3, 847}, {4, 131}, {20, 68}, {21, 915}, {22, 98}, {91, 759}, {94, 96}, {648, 933}, {842, 858}

▸ Functional Relations14 relations

• X₉₂₅ = reflection of X_i in X_j for these (i,j): (4, 131), (1300, 3)

• X₉₂₅ = isogonal conjugate of X₉₂₄

• X₉₂₅ = isotomic conjugate of X₆₅₆₃

• X₉₂₅ = trilinear pole of line X₅X₆

• X₉₂₅ = concurrence of reflections in sides of ABC of line X₄X₅₂

• X₉₂₅ = Ψ(X₁, X₉₁)

• X₉₂₅ = Ψ(X₃, X₆₈)

• X₉₂₅ = Ψ(X₄, X₅₂)

• X₉₂₅ = Ψ(X₆, X₅)

• X₉₂₅ = Λ(trilinear polar of X₂₄)

• X₉₂₅ = inverse-in-polar-circle of X₁₃₅

• X₉₂₅ = anticomplement of X₁₃₆

• X₉₂₅ = X₂₆-cross conjugate of X₂₅₀

• X₉₂₅ = Gibert-circumtangential conjugate of X₃₄₉₅₂