X₃₈₀₄

X₆₄₇com[INVERSE(nT(a², a² + c²))]

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

X₃₈₀₄ (X₆₄₇com[INVERSE(nT(a², a² + c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {187, 237}, {1499, 3265}

• Related Centers: X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X), X₂₃₇ (-LINE CONJUGATE OF X₂), X₁₄₉₉ (POINT BIHAM), X₃₂₆₅ (ISOTOMIC CONJUGATE OF X₁₀₇)

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(b^{2} - c^{2})(3a^{2} + b^{2} + c^{2})\)

Search Value (6, 9, 13): \(8.493058896640\)

▸ Incident Central Lines3 lines

{187, 237}, {1499, 3265}, {2525, 3566}