X₂₀₇₉

INVERSE-IN-CIRCUMCIRCLE OF X₁₁₅

X₂₀₇₉ = inverse-in-circumcircle of X₁₁₅

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

X₂₀₇₉ (INVERSE-IN-CIRCUMCIRCLE OF X₁₁₅) 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, 115}

• Related Centers: X₃ (CIRCUMCENTER), X₁₁₅ (CENTER OF KIEPERT HYPERBOLA)

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 = X₁₁₅

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

Search Value (6, 9, 13): \(-5.211780533714\)

X₂₀₇₉ lies on the tangential circle.

▸ Incident Central Lines7 lines

{3, 115}, {6, 1511}, {22, 111}, {24, 112}, {25, 1560}, {186, 230}, {187, 2070}

▸ Functional Relations4 relations

• X₂₀₇₉ = inverse-in-circumcircle of X₁₁₅

• X₂₀₇₉ = circumperp conjugate of X₃₈₇₃₈

• X₂₀₇₉ = Stammler-circle-inverse of X₃₈₇₃₃

• X₂₀₇₉ = center of bicevian conic of X₁₁₁₃ and X₁₁₁₄