X₃₅₃₅

EULER LINE INTERCEPT OF LINE X₂₇₅X_3317

X₃₅₃₅ = inverse-in-orthocentroidal-circle of X₃₅₃₆

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

X₃₅₃₅ (EULER LINE INTERCEPT OF LINE X₂₇₅X_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), {393, 590}

• Related Centers: X₁₁₅₁ (ISOGONAL CONJUGATE OF X₁₁₃₁), X₁₂₇₀ (ISOTOMIC CONJUGATE OF X₁₁₃₁), X₂ (CENTROID), X₃ (CIRCUMCENTER), X₃₉₃ (-CROSS CONJUGATE OF X₄), X₅₉₀ (ISOGONAL CONJUGATE OF X₅₈₈)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \sec A + 2 \csc A\)

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

Search Value (6, 9, 13): \(3.577350713683\)

▸ Incident Central Lines9 lines

{2, 3}, {275, 3317}, {281, 1659}, {393, 590}, {587, 1826}, {615, 3087}, {1249, 3068}, {1870, 3083}, {2052, 3316}

▸ Functional Relations3 relations

• X₃₅₃₅ = inverse-in-orthocentroidal-circle of X₃₅₃₆

• X₃₅₃₅ = X₁₁₅₁-cross conjugate of X₁₂₇₀

• X₃₅₃₅ = polar conjugate of X₁₁₃₁

Notes

As a point on the Euler line, X₃₅₃₅ has Shinagawa coefficients \((2F, S)\).