X506

4th ISOSCELIZER POINT

The isoscelizer equations
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_506 = 4th ISOSCELIZER POINT (0.5781, 0.2476) A B C X506 (a, b, c) = (5, 6, 7) | AB = 1

X506 (4th 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 \(f(A,B,C) = (\cos A/2)^{-2/3}\)
Barycentrics: \(af(A,B,C) : bf(B,C,A) : cf(C,A,B)\)
Search Value (6, 9, 13): \(1.341187212164\)
▸ Functional Relations1 relation

  • X506 = trilinear cube root of X7

Notes

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

have solution X = X506. (Peter Yff, 4/9/99)