X₇₀

ISOGONAL CONJUGATE OF X₂₆

X₇₀ is the isogonal conjugate of X₂₆.

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

X₇₀ (ISOGONAL CONJUGATE OF X₂₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {74, 1288}, {6, 1594}

• Related Centers: X₂₆ (CIRCUMCENTER OF THE TANGENTIAL TRIANGLE), X₇₄ (ISOGONAL CONJUGATE OF EULER INFINITY POINT), X₁₂₈₈ (COLLINGS TRANSFORM OF X₂₄), X₆ (SYMMEDIAN POINT), X₁₅₉₄ (RIGBY-LALESCU ORTHOPOLE)

Trilinears: \(bc/[b^{2} \cos 2B + c^{2} \cos 2C - a^{2} \cos 2A] : :\)

Barycentrics: \(1/(a^{8} - 2 a^{6} (b^{2} + c^{2}) + 2 a^{2} (b^{6} + c^{6}) - (b^{2} - c^{2})^{2} (b^{4} + c^{4})) : :\)

Search Value (6, 9, 13): \(5.721069014472\)

▸ Linear Combinations1 combination

• X₇₀ = \((S \cot \omega - 2R^{2})/(S \cot \omega -3 R^{2})\) X₃ - X₈₉₀₇ (Peter Moses, December 28, 2015)

X₇₀ lies on the Jerabek circumhyperbola.

▸ Incident Central Lines14 lines

{3, 8907}, {6, 1594}, {54, 1899}, {64, 6240}, {66, 6403}, {71, 2158}, {74, 1288}, {265, 6243}, {1176, 1352}, {1177, 3542}, {3448, 5504}, {3527, 7507}, {4846, 6241}, {6145, 6152}

▸ Functional Relations9 relations

• X₇₀ = isogonal conjugate of X₂₆

• X₇₀ = anticomplement of X₃₄₁₁₆

• X₇₀ = antigonal conjugate of X₃₈₅₃₄

• X₇₀ = X₅₇₁-crossconjugate of X₂

• X₇₀ = X_i-isoconjugate of X_j for these {i,j}: {1, 26}, {63, 8746}

• X₇₀ = reflection of the isogonal conjugate of X₂₀₇₂ in X₁₂₅

• X₇₀ = X₁₂₅-cevapoint of X₉₂₄

• X₇₀ = X₁₆₁-crosssum of X₈₅₅₃

• X₇₀ = barycentric product X₅₂₅ X₁₂₈₈