X₃₀₄₅

INTERSECTION X₅₄X_119∩X₁₀₀X_184

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

X₃₀₄₅ (INTERSECTION X₅₄X_119∩X₁₀₀X_184) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {11, 110}, {54, 119}

• Related Centers: X₁₁ (FEUERBACH POINT), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₅₄ (KOSNITA POINT), X₁₁₉ (FEUERBACH ANTIPODE)

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

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

Search Value (6, 9, 13): \(-1.020805305221\)

X₃₀₄₅ lies on the sine-triple-angle circle.

▸ Incident Central Lines6 lines

{11, 110}, {49, 952}, {54, 119}, {100, 184}, {2771, 3043}, {2805, 3048}