X₁₇₁

{X₂, X₃₁}-HARMONIC CONJUGATE OF X₂₃₈

X₁₇₁ is the {X₂, X₃₁}-harmonic conjugate of X₂₃₈.

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

X₁₇₁ ({X₂, X₃₁}-HARMONIC CONJUGATE OF X₂₃₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 3}, {2, 31}

• Related Centers: X₂₅₆ (1st SHARYGIN POINT), X₁ (INCENTER), X₃ (CIRCUMCENTER), X₂ (CENTROID), X₃₁ (2nd POWER POINT)

Trilinears: \(a^{2} + bc : b^{2} + ca : c^{2} + ab\)

Barycentrics: \(a^{3} + abc : b^{3} + abc : c^{3} + abc\)

Search Value (6, 9, 13): \(1.379817388436\)

▸ Incident Central Lines23 lines

{1, 3}, {2, 31}, {4, 601}, {6, 43}, {7, 983}, {10, 58}, {37, 846}, {42, 81}, {47, 498}, {63, 612}, {72, 1046}, {84, 989}, {98, 109}, {181, 511}, {222, 611}, {292, 893}, {319, 757}, {385, 894}, {388, 603}, {474, 978}, {595, 1125}, {602, 631}, {756, 896}

▸ Functional Relations13 relations

• X₁₇₁ = isogonal conjugate of X₂₅₆

• X₁₇₁ = isotomic conjugate of X₇₀₁₈

• X₁₇₁ = complement of X₄₃₈₈

• X₁₇₁ = anticomplement of X₃₈₄₆

• X₁₇₁ = perspector of Gemini triangle 33 and cross-triangle of ABC and Gemini triangle 33

• X₁₇₁ = trilinear pole line X₃₂₈₇X₃₈₀₅ (the perspectrix of ABC and Gemini triangle 34)

• X₁₇₁ = X₂₉₂-Ceva conjugate of X₂₃₈

• X₁₇₁ = X_i-beth conjugate of X_j for these (i,j): (100, 171), (643, 42)

• X₁₇₁ = crosssum of PU(6)

• X₁₇₁ = crosspoint of PU(8)

• X₁₇₁ = intersection of tangents at PU(8) to hyperbola {A, B, C,X₁₀₀,PU(8)}}

• X₁₇₁ = {X₁,X₄₀}-harmonic conjugate of X₃₇₅₉₈

• X₁₇₁ = {X₅₅,X₅₆}-harmonic conjugate of X₂₃₈₅₃