X₁₅₀₇

1st MORLEY-GIBERT POINT

X₁₅₀₇ and X₁₅₀₈ are centers on Morley cubic, which also passes through X₃₅₆, X₃₅₇, X₃₅₈; see Bernard Gibert’s site.

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

X₁₅₀₇ (1st MORLEY-GIBERT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 358}

• Related Centers: X₁ (INCENTER), X₃₅₈ (2nd MORLEY-TAYLOR-MARR CENTER)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = 1 + 2(\cos B/3 + \cos C/3 - \cos A/3)\)

Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)

Search Value (6, 9, 13): \(1.445293141199\)

▸ Incident Central Lines1 line

{1, 358}

▸ Functional Relations2 relations

• X₁₅₀₇ = SS(A→A/3) of X₃₃₃₆

• X₁₅₀₇ = perspector of excentral and 1st Morley triangles