X₂₄₁₅

GIBERT-SIMSON TRANSFORM OF X₁₂₉₃

X₂₄₁₅ = cevapoint of X₉₀₀ and X₂₃₂₅

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

X₂₄₁₅ (GIBERT-SIMSON TRANSFORM OF X₁₂₉₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Related Centers: X₂₄₄₁ (ISOGONAL CONJUGATE OF X₂₄₁₅)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(2a - b - c)/[(b - c)(3a - b - c)]\) (M. Iliev, 5/13/07)

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

Search Value (6, 9, 13): \(6.196392790279\)

X₂₄₁₅ lies on the cubic K010.

▸ Functional Relations4 relations

• X₂₄₁₅ = isogonal conjugate of X₂₄₄₁

• X₂₄₁₅ = isotomic conjugate of X₂₄₀₃

• X₂₄₁₅ = cevapoint of X₉₀₀ and X₂₃₂₅

• X₂₄₁₅ = trilinear pole of line X₁₂₁X₅₁₉ (the Simson line of X₁₂₉₃)