X₁₄₉₂

COLUMBUS POINT

X₁₄₉₂ = cevapoint of X₅₁₃ and X₁₃₈₆

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

X₁₄₉₂ (COLUMBUS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {101, 660}, {190, 692}

• Related Centers: X₅₁₃ (ISOGONAL CONJUGATE OF X₁₀₀), X₁₃₈₆ (MIDPOINT OF INCENTER AND SYMMEDIAN POINT), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₆₆₀ (TRILINEAR POLE OF LINE X₁X₃₉), X₁₉₀ (YFF PARABOLIC POINT), X₆₉₂ (-CEVA CONJUGATE OF X₁₀₁)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/(b^{3} - c^{3})\)

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

Search Value (6, 9, 13): \(1.295559745713\)

▸ Incident Central Lines5 lines

{88, 985}, {100, 825}, {101, 660}, {110, 789}, {190, 692}

▸ Functional Relations5 relations

• X₁₄₉₂ = isogonal conjugate of X₁₄₉₁

• X₁₄₉₂ = cevapoint of X₅₁₃ and X₁₃₈₆

• X₁₄₉₂ = X_i-cross conjugate of X_j for these (i,j): (182, 59), (1491, 1)

• X₁₄₉₂ = trilinear pole of line X₁X₃₂

• X₁₄₉₂ = trilinear product of circumcircle intercepts of line X₂X₃₁