X₅₀₈

6th ISOSCELIZER POINT

The isoscelizer equations

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

X₅₀₈ (6th ISOSCELIZER POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Trilinears: \(a^{-1/2}\sec(A/2) : b^{-1/2}\sec(B/2) : c^{-1/2}\sec(C/2)\)

Barycentrics: \(a^{1/2}\sec(A/2) : b^{1/2}\sec(B/2) : c^{1/2}\sec(C/2)\)

Search Value (6, 9, 13): \(1.548710508717\)

▸ Functional Relations3 relations

• X₅₀₈ = trilinear product X₃₆₆*X₁₇₄

• X₅₀₈ = trilinear square root of X₈₅

• X₅₀₈ = barycentric square root of X₇

Notes

a[area of T(A,X)] = b[area of T(B,X)] = c[area of T(C,X)]

have solution X = X₅₀₈. (Peter Yff, 4/9/99)