X₁₁₃₆

5th MORLEY-TAYLOR-MARR CENTER

X₁₁₃₆ = perspector of ABC and 2nd Morley triangle

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

X₁₁₃₆ (5th MORLEY-TAYLOR-MARR CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Related Centers: X₁₁₃₇ (6th MORLEY-TAYLOR-MARR CENTER)

Trilinears: \(1/\cos(A/3 + 4\pi /3) : :\)

Search Value (6, 9, 13): \(-3.920160941226\)

▸ Alternate Coordinates2 forms

• Trilinears: \(\sec(A/3 + \pi /3) :\)

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

▸ Functional Relations3 relations

• X₁₁₃₆ = isogonal conjugate of X₁₁₃₇

• X₁₁₃₆ = perspector of ABC and 2nd Morley triangle

• X₁₁₃₆ = trilinear product of vertices of 2nd Morley triangle

Notes

See the reference at X₁₁₃₄.

Another construction, by Seiichi Kirikami, appears at Hyacinthos 21423 (January 16, 2013), posted by Chris van Tienhoven.