X₃₀₄₆

INTERSECTION X₅₄X_118∩X₁₀₁X_184

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

X₃₀₄₆ (INTERSECTION X₅₄X_118∩X₁₀₁X_184) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {54, 118}, {101, 184}

• Related Centers: X₅₄ (KOSNITA POINT), X₁₁₈ (MIDPOINT OF X₄ AND X₁₀₁), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₁₈₄ (INVERSE OF X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{3}(a^{3} + b^{3} - c^{3} - a^{2}b - ab^{2} + bc^{2})(a^{3} - b^{3} + c^{3} - a^{2}c - ac^{2} + b^{2}c)\)

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

Search Value (6, 9, 13): \(-1.732638279648\)

X₃₀₄₆ lies on the sine-triple-angle circle.

▸ Incident Central Lines9 lines

{49, 2808}, {54, 118}, {101, 184}, {103, 1147}, {215, 3022}, {2772, 3043}, {2774, 3047}, {2786, 3044}, {2813, 3048}