X₁₀₃₈

INTERSECTION OF LINES X₁X_3 AND X₂X_34

X₁₀₃₈ = homothetic center of 6th anti-mixtilinear triangle and anti-tangential midarc triangle

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

X₁₀₃₈ (INTERSECTION OF LINES X₁X_3 AND X₂X_34) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 3}, {2, 34}

• Related Centers: X₁₀₃₉ (ISOGONAL CONJUGATE OF X₁₀₃₈), X₁ (INCENTER), X₃ (CIRCUMCENTER), X₂ (CENTROID), X₃₄ (-BETH CONJUGATE OF X₄)

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

Search Value (6, 9, 13): \(-7.816033297835\)

▸ Alternate Coordinates1 form

• Trilinears: \(1 + \sec B \sec C : :\)

▸ Incident Central Lines18 lines

{1, 3}, {2, 34}, {4, 1076}, {9, 478}, {20, 33}, {21, 1041}, {38, 1106}, {63, 201}, {69, 73}, {72, 222}, {172, 577}, {221, 960}, {223, 936}, {225, 377}, {226, 975}, {278, 443}, {388, 612}, {1068, 1074}

▸ Functional Relations2 relations

• X₁₀₃₈ = isogonal conjugate of X₁₀₃₉

• X₁₀₃₈ = homothetic center of 6th anti-mixtilinear triangle and anti-tangential midarc triangle

Notes

X₁₀₃₈ is the {X₁,X₃}-harmonic conjugate of X₁₀₄₀.