X₃₈₅₅

X₃₅₂₅com(EULER TRIANGLE)

X₃₈₅₅ = orthocentroidal circle inverse of X₃₅₂₉

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

X₃₈₅₅ (X₃₅₂₅com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {946, 3632}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₉₄₆ (MIDPOINT OF X₁ AND X₄), X₃₆₃₂ (H-1(X₈; M, 1/2))

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 3a^{4} - 7b^{4} - 7c^{4} + 4a^{2}b^{2} + 4a^{2}c^{2} + 14b^{2}c^{2}\)

Search Value (6, 9, 13): \(-1.146080390882\)

▸ Incident Central Lines3 lines

{2, 3}, {944, 3636}, {946, 3632}

▸ Functional Relations4 relations

• X₃₈₅₅ = anticomplement of X₁₅₇₂₀

• X₃₈₅₅ = {X₂,X₄}-harmonic conjugate of X₃₅₂₉

• X₃₈₅₅ = {X₂,X₂₀}-harmonic conjugate of X₃₅₃₀

• X₃₈₅₅ = orthocentroidal circle inverse of X₃₅₂₉

Notes

As a point on the Euler line, X₃₈₅₅ has Shinagawa coefficients \((2, 5)\).