X₂₃₀₇

X₂-ISOCONJUGATE OF X₁₂₅₁

X₂₃₀₇ = X₁₀₈₂-Ceva conjugate of X₁₂₅₀

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

X₂₃₀₇ (X₂-ISOCONJUGATE OF X₁₂₅₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {6, 41}, {15, 35}

• Related Centers: X₁₀₈₂ (POINT ALPHERATZ), X₁₂₅₀ (ISOGONAL CONJUGATE OF X₁₀₈₁), X₆ (SYMMEDIAN POINT), X₄₁ (-CEVA CONJUGATE OF X₃₁), X₁₅ (1st ISODYNAMIC POINT), X₃₅ ({X)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₂₅₁

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(2.471760410692\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (\sin A/2) \cos(A/2 + \pi /6)\)

▸ Incident Central Lines7 lines

{1, 61}, {6, 41}, {11, 398}, {12, 396}, {15, 35}, {36, 62}, {65, 2153}

▸ Functional Relations1 relation

• X₂₃₀₇ = X₁₀₈₂-Ceva conjugate of X₁₂₅₀