X₃₂₃₁

ISOGONAL CONJUGATE OF X₃₂₂₈

X₃₂₃₁ is the isogonal conjugate of X₃₂₂₈.

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

X₃₂₃₁ (ISOGONAL CONJUGATE OF X₃₂₂₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3124, 3291}

• Related Centers: X₃₁₂₄ (DANNEELS PERSPECTOR FOR X₇₆), X₃₂₉₁ (INTERSECTION OF LINES X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(2b^{2}c^{2} - a^{2}b^{2} - a^{2}c^{2})\)

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

Search Value (6, 9, 13): \(-2.541040288956\)

▸ Incident Central Lines6 lines

{2, 6}, {23, 2076}, {110, 1691}, {111, 694}, {187, 237}, {468, 2211}

▸ Functional Relations12 relations

• X₃₂₃₁ = reflection of X₃₁₂₄ in X₃₂₉₁

• X₃₂₃₁ = isogonal conjugate of X₃₂₂₈

• X₃₂₃₁ = isotomic conjugate of X₃₄₀₈₇

• X₃₂₃₁ = isotomic conjugate of isogonal conjugate of X₃₃₈₇₅

• X₃₂₃₁ = complement of anticomplementary conjugate of X₃₉₃₆₁

• X₃₂₃₁ = X₂-Ceva conjugate of X₃₈₉₉₈

• X₃₂₃₁ = perspector of hyperbola {{A, B, C,X₆,X₉₉}}

• X₃₂₃₁ = X₇₂₉-Ceva conjugate of X₆

• X₃₂₃₁ = crosssum of X_i and X_j for these (i,j): (2, 538), (512, 1645), (888, 1084)

• X₃₂₃₁ = crossdifference of every pair of points on the line X₂X₅₁₂

• X₃₂₃₁ = trilinear pole of line X₈₈₇X₈₈₈

• X₃₂₃₁ = inverse-in-Parry-isodynamic-circle of X₅₀₂₇; see X₂