X₃₅₃₃

EULER LINE INTERCEPT OF LINE X₃₇₁X_3317

X₃₅₃₃ = pole of Napoleon axis wrt conic {{X₂,X₁₅,X₁₆,X₁₇,X₁₈}}

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

X₃₅₃₃ (EULER LINE INTERCEPT OF LINE X₃₇₁X_3317) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {371, 3317}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₃₇₁ (KENMOTU POINT), X₃₃₁₇ (ISOGONAL CONJUGATE OF X₃₃₁₂)

Trilinears: \(6 \cos A + 5 \cos B \cos C : :\)

Barycentrics: \(\cot B \cot C - 6 : :\)

Search Value (6, 9, 13): \(3.117956333866\)

▸ Alternate Coordinates1 form

• Trilinears: \(5 \sec A + 6 \sec B \sec C : :\)

▸ Incident Central Lines3 lines

{2, 3}, {371, 3317}, {372, 3316}

▸ Functional Relations1 relation

• X₃₅₃₃ = pole of Napoleon axis wrt conic {{X₂,X₁₅,X₁₆,X₁₇,X₁₈}}

Notes

As a point on the Euler line, X₃₅₃₃ has Shinagawa coefficients \((6, -1)\).