X₃₉₄₆

X₁₃₈₆com[INVERSE(n(HEXYL TRIANGLE))]

X₃₉₄₆ = complement of X₂₃₂₁

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

X₃₉₄₆ (X₁₃₈₆com[INVERSE(n(HEXYL TRIANGLE))]) 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, 2321}

• Related Centers: X₂ (CENTROID), X₂₃₂₁ (-ISOCONJUGATE OF X₁₄₀₈)

Barycentrics: \(2a^{2} + b^{2} + c^{2} + ab + ac - 2bc : :\)

Search Value (6, 9, 13): \(1.516943534128\)

▸ Incident Central Lines22 lines

{1, 142}, {2, 2321}, {6, 527}, {7, 1419}, {9, 3672}, {37, 3008}, {57, 347}, {81, 553}, {141, 519}, {192, 2325}, {239, 1654}, {284, 1429}, {516, 1386}, {536, 3589}, {740, 1125}, {894, 1266}, {950, 3100}, {1086, 1100}, {1323, 1418}, {2324, 2999}, {3618, 3729}, {3634, 3773}

▸ Functional Relations10 relations

• X₃₉₄₆ = isogonal conjugate of X₃₈₈₂₅

• X₃₉₄₆ = complement of X₂₃₂₁

• X₃₉₄₆ = crosspoint of X₂ and X₁₄₃₄

• X₃₉₄₆ = crosssum of X₆ and X₁₃₃₄

• X₃₉₄₆ = X₂-Ceva conjugate of X₃₈₉₃₀

• X₃₉₄₆ = X_i-isoconjugate of X_j for these {i,j}: {1, 38825}, {210, 38811}

• X₃₉₄₆ = trilinear product X_i*X_j for these {i,j}: {9, 10521}, {81, 4854}, {100, 23729}

• X₃₉₄₆ = trilinear quotient X_i/X_j for these (i,j): (1, 38825), (1014, 38811), (4854, 37), (10521, 57), (23729, 513)

• X₃₉₄₆ = barycentric product X_i*X_j for these {i,j}: {8, 10521}, {86, 4854}, {190, 23729}

• X₃₉₄₆ = barycentric quotient X_i/X_j for these (i,j): (6, 38825), (1412, 38811), (4854, 10), (10521, 7), (23729, 514)