X₃₈₁₄

X₂₀₇₇com(EULER TRIANGLE)

X₃₈₁₄ = nine-point-circle-inverse of X₁₀

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

X₃₈₁₄ (X₂₀₇₇com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {5, 10}, {2, 36}

• Related Centers: X₅ (NINE-POINT CENTER), X₁₀ (SPIEKER CENTER), X₂ (CENTROID), X₃₆ (INVERSE-IN-CIRCUMCIRCLE OF INCENTER)

Barycentrics: \((b^{2}+c^{2}) a^{2}-(b+c) b c a-(b^{2}-c^{2})^{2} : :\)

Search Value (6, 9, 13): \(5.231696582063\)

▸ Linear Combinations2 combinations

• X₃₈₁₄ = \(2r\) X₅ - \(R\) X₁₀

• X₃₈₁₄ = \(3\) X₂ - X₃₆ (Peter Moses, April 2, 2012)

▸ Incident Central Lines30 lines

{2, 36}, {4, 2077}, {5, 10}, {11, 519}, {12, 1125}, {30, 3035}, {100, 3583}, {115, 1575}, {119, 214}, {121, 3259}, {381, 1376}, {403, 1861}, {404, 3585}, {427, 1878}, {442, 1155}, {484, 1698}, {495, 551}, {496, 3244}, {498, 2478}, {499, 3436}, {516, 1532}, {758, 908}, {958, 1656}, {1107, 1506}, {1621, 3584}, {1739, 3120}, {2392, 3142}, {2550, 3545}, {2551, 3090}, {3836, 4129}

▸ Functional Relations7 relations

• X₃₈₁₄ = isotomic conjugate of isogonal conjugate of X₂₀₉₆₂

• X₃₈₁₄ = polar conjugate of isogonal conjugate of X₂₂₀₅₉

• X₃₈₁₄ = {X₅,X₁₀}-harmonic conjugate of X₂₅₆₃₉

• X₃₈₁₄ = nine-point-circle-inverse of X₁₀

• X₃₈₁₄ = complement of X₃₆

• X₃₈₁₄ = complementary conjugate of X₂₁₄

• X₃₈₁₄ = inverse-in-excircles-radical-circle of X₉₇₀