X₁₀₉₀

TRILINEAR SQUARE OF X₁₁

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

X₁₀₉₀ (TRILINEAR SQUARE OF X₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {11, 523}, {5, 1091}

• Related Centers: X₁₁ (FEUERBACH POINT), X₅₂₃ (ISOGONAL CONJUGATE OF X₁₁₀), X₅ (NINE-POINT CENTER), X₁₀₉₁ (TRILINEAR SQUARE OF X₁₂)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = [1 - \cos(B - C)]^{2}\)

Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)

Search Value (6, 9, 13): \(2.289921993276\)

▸ Incident Central Lines2 lines

{5, 1091}, {11, 523}