X₂₀₇₄

INVERSE-IN-CIRCUMCIRCLE OF X₂₈

X₂₀₇₄ = inverse-in-circumcircle of X₂₈

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

X₂₀₇₄ (INVERSE-IN-CIRCUMCIRCLE OF X₂₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Circle: Circumcircle (circumcircle) — Passes through vertices A, B, C; centered at X₃ CIRCUMCENTER

• Central Lines: {3, 28}, {2, 3} (Euler line)

• Related Centers: X₃ (CIRCUMCENTER), X₂₈ (CEVAPOINT OF X₁₉ AND X₂₅), X₂ (CENTROID)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as noted just above X₂₀₇₀ using X = X₂₈

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(1.443426247961\)

▸ Incident Central Lines6 lines

{2, 3}, {104, 1304}, {105, 935}, {110, 912}, {162, 1870}, {476, 915}

▸ Functional Relations1 relation

• X₂₀₇₄ = inverse-in-circumcircle of X₂₈

Notes

As a point on the Euler line, X₂₀₇₄ has Shinagawa coefficients \((abc\$a\$F(R/|OX|)^{2} - [2\$a\$(E + F) - \$a^{3}\$ + 2abc]FS{1 - (R/|OX|)^{2}}, -[abc\$a\$(E+F) + ES^{2}](R/|OX|)^{2} + [2\$a\$(E+F) - \$a^{3}\$ + 2abc]FS{1 - (R/|OX|)^{2}})\).