X₆₉₂

X₁₁₀-CEVA CONJUGATE OF X₁₀₁

X₆₉₂ = isogonal conjugate of X₆₉₃

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

X₆₉₂ (X₁₁₀-CEVA CONJUGATE OF X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {100, 110}, {55, 184}

• Related Centers: X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₅₅ (INSIMILICENTER), X₁₈₄ (INVERSE OF X)

Trilinears: \(a^{2}/(b - c) : b^{2}/(c - a) : c^{2}/(a - b)\)

Barycentrics: \(a^{3}/(b - c) : b^{3}/(c - a) : c^{3}/(a - b)\)

Search Value (6, 9, 13): \(0.624397084465\)

▸ Incident Central Lines14 lines

{25, 913}, {48, 911}, {55, 184}, {59, 513}, {99, 785}, {100, 110}, {101, 926}, {154, 197}, {163, 906}, {182, 1001}, {206, 219}, {213, 923}, {667, 1110}, {813, 825}

▸ Functional Relations16 relations

• X₆₉₂ = isogonal conjugate of X₆₉₃

• X₆₉₂ = isotomic conjugate of complement of polar conjugate of isogonal conjugate of X₂₃₁₉₁

• X₆₉₂ = isotomic conjugate of anticomplement of polar conjugate of isogonal conjugate of X₂₃₂₂₈

• X₆₉₂ = complement of X₂₁₂₉₃

• X₆₉₂ = anticomplement of X₂₁₂₅₂

• X₆₉₂ = X_i-Ceva conjugate of X_j for these (i,j): (59, 6), (110, 101)

• X₆₉₂ = cevapoint of X_i and X_j for these (i,j): (101, 109), (110, 163)

• X₆₉₂ = crosssum of X_i and X_j for these (i,j): (2, 149), (513, 905), (514, 522), (764, 1086)

• X₆₉₂ = crossdifference of every pair of points on line X₉₁₈X₁₀₈₆

• X₆₉₂ = barycentric product of PU(i) for i in (26, 49)

• X₆₉₂ = barycentric product of circumcircle intercepts of line X₁X₆

• X₆₉₂ = barycentric product X₆*X₁₀₀

• X₆₉₂ = trilinear pole of line X₃₁X₃₂

• X₆₉₂ = X₉₂-isoconjugate of X₉₀₅

• X₆₉₂ = trilinear product of circumcircle intercepts of line X₆X₃₁

• X₆₉₂ = trilinear product X₆*X₁₀₁

Notes

Let A'B'C' be the triangle described in ADGEOM #2697 (8/26/2015, Tran Quang Hung). A'B'C' is homothetic to the anti-Mandart-incircle triangle at X₆₉₂. (Randy Hutson, January 15, 2019)