X₃₀₄₂

COMPLEMENT OF X₁₃₆₄

X₃₀₄₂ is the complement of X₁₃₆₄.

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

X₃₀₄₂ (COMPLEMENT OF X₁₃₆₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3040, 10}

• Related Centers: X₃₀₄₀ (COMPLEMENT OF X₁₃₆₁), X₁₀ (SPIEKER CENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[(a - b + c)(a - c)^{2}\cos^{2} B + (a + b - c)(a - b)^{2}\cos^{2} C]\)

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

Search Value (6, 9, 13): \(2.344319248874\)

X₃₀₄₂ lies on the Spieker circle.

▸ Incident Central Lines13 lines

{2, 1364}, {8, 1361}, {10, 2818}, {72, 1845}, {102, 958}, {109, 1376}, {117, 1329}, {118, 124}, {151, 2551}, {474, 1795}, {960, 2817}, {2814, 3039}, {2815, 3039}

▸ Functional Relations3 relations

• X₃₀₄₂ = midpoint of X_i and X_j for these (i,j): (8, 1361), (72, 1845)

• X₃₀₄₂ = reflection of X₃₀₄₀ in X₁₀

• X₃₀₄₂ = complement of X₁₃₆₄