X₅₉

ISOGONAL CONJUGATE OF X₁₁

X₅₉ is the isogonal conjugate of X₁₁.

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

X₅₉ (ISOGONAL CONJUGATE OF X₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {100, 521}, {101, 657}

• Related Centers: X₁₁ (FEUERBACH POINT), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₅₂₁ (ISOGONAL CONJUGATE OF X₁₀₈), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₆₅₇ (CROSSDIFFERENCE OF X₁ AND X₇)

Trilinears: \(1/[1 - \cos(B - C)] : 1/[1 - \cos(C - A)] : 1/[1 - \cos(A - B)]\)

Barycentrics: \(a/[1 - \cos(B - C)] : b/[1 - \cos(C - A)] : c/[1 - \cos(A - B)]\)

Search Value (6, 9, 13): \(0.114418313907\)

▸ Alternate Coordinates1 form

• Trilinears: \(\csc^{2} (B/2 - C/2) : :\)

▸ Incident Central Lines8 lines

{36, 1110}, {60, 1101}, {100, 521}, {101, 657}, {109, 901}, {513, 651}, {518, 765}, {523, 655}

▸ Functional Relations12 relations

• X₅₉ = isogonal conjugate of X₁₁

• X₅₉ = isotomic conjugate of X₃₄₃₈₇

• X₅₉ = cevapoint of X_i and X_j for these (i,j): (55, 101), (56, 109), (1381, 1382)

• X₅₉ = X_i-cross conjugate of X_j for these (i,j): (1, 110), (3, 100), (55, 101), (56, 109), (182, 1492)

• X₅₉ = crossdifference of every pair of points on line X₄₅₃₀X_14393

• X₅₉ = X₇₆₅-beth conjugate of X₇₆₅

• X₅₉ = trilinear pole of line X₁₀₁X₁₀₉

• X₅₉ = perspector of ABC and the reflection of the intouch triangle in line X₁X₃

• X₅₉ = perspector of ABC and extraversion triangle of X₆₀

• X₅₉ = X₇₅-isoconjugate of X₃₂₇₁

• X₅₉ = trilinear square of X₆₇₃₃

• X₅₉ = complement of isogonal conjugate of X₃₆₉₀₂