X₂₀₇₅

INVERSE-IN-CIRCUMCIRCLE OF X₂₉

X₂₀₇₅ = inverse-in-circumcircle of X₂₉

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

X₂₀₇₅ (INVERSE-IN-CIRCUMCIRCLE OF X₂₉) 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, 29}, {2, 3} (Euler line)

• Related Centers: X₃ (CIRCUMCENTER), X₂₉ (CEVAPOINT OF INCENTER AND ORTHOCENTER), 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 = X₂₉

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

Search Value (6, 9, 13): \(-20.375744938032\)

▸ Incident Central Lines5 lines

{2, 3}, {36, 162}, {102, 1304}, {250, 1101}, {935, 1311}

▸ Functional Relations1 relation

• X₂₀₇₅ = inverse-in-circumcircle of X₂₉

Notes

As a point on the Euler line, X₂₀₇₅ has Shinagawa coefficients \(([\$a\$S^{2} - \$aS_{B}S_{C}\$ - 2\$aS_{A}\$F]FS^{2}{1 - (R/|OX|)^{2}} + abc[2F^{2}S^{2} + (E - 2F)FS^{2}](R/|OX|)^{2}, -[\$a\$S^{2} + \$aS_{B}S_{C}\$ + 2\$aS_{A}\$F]FS^{2}{1 - (R/|OX|)^{2}} + abc[2F^{2}S^{2} + {(E - 2F)FS^{2} - E\$bcS_{B}S_{C}\$}](R/|OX|)^{2})\).