X₁₁₃₄

3rd MORLEY-TAYLOR-MARR CENTER

X₁₁₃₄ = perspector of ABC and 3rd Morley triangle

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

X₁₁₃₄ (3rd MORLEY-TAYLOR-MARR CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {356, 1135}, {357, 3275}

• Related Centers: X₁₁₃₅ (4th MORLEY-TAYLOR-MARR CENTER), X₃₅₆ (MORLEY CENTER), X₃₅₇ (1st MORLEY-TAYLOR-MARR CENTER), X₃₂₇₅ (PERSPECTOR OF TRIANGLES S1S2S3 AND J1J2J3)

Trilinears: \(1/\cos(A/3 + 2\pi /3) : :\)

Search Value (6, 9, 13): \(2.082095643900\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines2 lines

{356, 1135}, {357, 3275}

▸ Functional Relations3 relations

• X₁₁₃₄ = isogonal conjugate of X₁₁₃₅

• X₁₁₃₄ = perspector of ABC and 3rd Morley triangle

• X₁₁₃₄ = trilinear product of vertices of 3rd Morley triangle

Notes

F. Glanville Taylor and W. L. Marr, “The six trisectors of each of the angles of a triangle,” Proceedings of the Edinburgh Mathematical Society 33 (1913-14) 119-131; especially item 9, p. 127.