X₅₀₇

5th ISOSCELIZER POINT

The isoscelizer equations

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

X₅₀₇ (5th ISOSCELIZER POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

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

Barycentrics: \(af(A,B,C) : bf(B,C,A) : cf(C,A,B)\)

Search Value (6, 9, 13): \(1.426982771047\)

▸ Functional Relations1 relation

• X₅₀₇ = trilinear square root of X₁₇₄

Notes

\([\operatorname{area} of T(A,X)][X(A)]^{2} = [\operatorname{area} of T(B,X)][X(B)]^{2} = [\operatorname{area} of T(C,X)][X(C)]^{2}\)

have solution X = X₅₀₇. (Peter Yff, 4/9/99)