X₁₂₁₂

ISOGONAL CONJUGATE OF X₁₁₇₀

X₁₂₁₂ is the isogonal conjugate of X₁₁₇₀.

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

X₁₂₁₂ (ISOGONAL CONJUGATE OF X₁₁₇₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Medial Triangle △M_aM_bM_c — vertices M_a, M_b, M_c (Formed by the midpoints of sides BC, CA, AB)

• Central Lines: {2, 85}

• Related Centers: X₂ (CENTROID), X₈₅ (ISOTOMIC CONJUGATE OF X₉)

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

Search Value (6, 9, 13): \(3.259199785525\)

▸ Incident Central Lines7 lines

{1, 6}, {2, 85}, {3, 169}, {10, 1146}, {21, 294}, {65, 672}, {281, 475}

▸ Functional Relations10 relations

• X₁₂₁₂ = isogonal conjugate of X₁₁₇₀

• X₁₂₁₂ = complement of X₈₅

• X₁₂₁₂ = X_i-Ceva conjugate of X_j for these (i,j) : (2, 142), (142, 354)

• X₁₂₁₂ = crosspoint of X_i and X_j for these (i,j): (1, 277), (2, 9)

• X₁₂₁₂ = crosssum of X_i and X_j for these (i,j): (1, 218), (6, 57)

• X₁₂₁₂ = isotomic conjugate of X₃₁₆₁₈

• X₁₂₁₂ = polar conjugate of isogonal conjugate of X₂₂₀₇₉

• X₁₂₁₂ = {X₁,X₉}-harmonic conjugate of X₂₂₀

• X₁₂₁₂ = perspector of circumconic centered at X₁₄₂

• X₁₂₁₂ = center of circumconic that is locus of trilinear poles of lines passing through X₁₄₂