X₁₁₃₇

6th MORLEY-TAYLOR-MARR CENTER

X₁₁₃₇ = perspector of ABC and 2nd Morley adjunct triangle

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

X₁₁₃₇ (6th MORLEY-TAYLOR-MARR CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {16, 358}

• Related Centers: X₁₁₃₆ (5th MORLEY-TAYLOR-MARR CENTER), X₁₆ (2nd ISODYNAMIC POINT), X₃₅₈ (2nd MORLEY-TAYLOR-MARR CENTER)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \cos(A/3 + 4\pi /3)\)

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

Search Value (6, 9, 13): \(6.347013547244\)

▸ Alternate Coordinates1 form

• Trilinears: \(\cos(A/3 + \pi /3) : \cos(B/3 + \pi /3) : \cos(C/3 + \pi /3)\)

▸ Incident Central Lines1 line

{16, 358}

▸ Functional Relations3 relations

• X₁₁₃₇ = isogonal conjugate of X₁₁₃₆

• X₁₁₃₇ = perspector of ABC and 2nd Morley adjunct triangle

• X₁₁₃₇ = trilinear product of vertices of 2nd Morley adjunct triangle

Notes

See the reference at X₁₁₃₄.