X₁₃₅₆

BRISSE TRANSFORM OF X₉₉

X₁₃₅₆ = trilinear product X₅₇*X₁₀₈₄

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

X₁₃₅₆ (BRISSE TRANSFORM OF X₉₉) 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, 3037}

• Related Centers: X₂ (CENTROID), X₃₀₃₇ (COMPLEMENT OF X₁₃₅₆)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as above X₁₃₅₄, using X = X₉₉

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

Search Value (6, 9, 13): \(0.120238186770\)

X₁₃₅₆ lies on the incircle.

▸ Incident Central Lines1 line

{56, 741}

▸ Functional Relations3 relations

• X₁₃₅₆ = anticomplement of X₃₀₃₇

• X₁₃₅₆ = trilinear product X₅₇*X₁₀₈₄

• X₁₃₅₆ = barycentric product X₇*X₁₀₈₄