X₃₈₃₉

X₃₅₄₅com(EULER TRIANGLE)

X₃₈₃₉ = trisector nearest X₄ of segment X₂X₄

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

X₃₈₃₉ (X₃₅₄₅com(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), {147, 671}

• Related Centers: X₂ (CENTROID), X₃ (CIRCUMCENTER), X₄ (ORTHOCENTER), X₁₄₇ (TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE), X₆₇₁ (TRILINEAR POLE OF LINE X₂X₅₂₃)

Barycentrics: \(5a^{4} - 7b^{4} - 7c^{4} + 2a^{2}b^{2} + 2a^{2}c^{2} + 14 b^{2}c^{2} : :\)

Search Value (6, 9, 13): \(-2.907956676455\)

▸ Linear Combinations1 combination

• X₃₈₃₉ = \(7\) X₂ - \(4\) X₃

▸ Incident Central Lines12 lines

{2, 3}, {145, 3656}, {147, 671}, {390, 3583}, {519, 1699}, {598, 3424}, {946, 3241}, {962, 3679}, {1131, 1328}, {1132, 1327}, {3585, 3600}, {3622, 3655}

▸ Functional Relations4 relations

• X₃₈₃₉ = circumcircle-inverse of X₃₇₉₅₇

• X₃₈₃₉ = {X₂,X₃}-harmonic conjugate of X₁₅₇₂₁

• X₃₈₃₉ = trisector nearest X₄ of segment X₂X₄

• X₃₈₃₉ = endo homothetic center of Ehrmann side-triangle and submedial triangle; the homothetic center is X₅₀₅₅

Notes

As a point on the Euler line, X₃₈₃₉ has Shinagawa coefficients \((1, 6)\).