X₁₅₀₈

2nd MORLEY-GIBERT POINT

X₁₅₀₈ is the perspector of the excentral tiangle and the 1st Morley adjunct triangle. (César Lozada, January 18, 2015)

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

X₁₅₀₈ (2nd MORLEY-GIBERT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 357}

• Related Centers: X₁ (INCENTER), X₃₅₇ (1st MORLEY-TAYLOR-MARR CENTER)

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

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

Search Value (6, 9, 13): \(1.844382327844\)

▸ Incident Central Lines1 line

{1, 357}

▸ Functional Relations2 relations

• X₁₅₀₈ = SS(A → A/3) of X₃₄₆₈

• X₁₅₀₈ = perspector of excentral and 1st Morley adjunct triangles

Notes

See the notes at X₁₅₀₇ and X₃₅₆.