X₂₅₉

ISOGONAL CONJUGATE OF X₁₇₄

X₂₅₉ is the isogonal conjugate of X₁₇₄.

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

X₂₅₉ (ISOGONAL CONJUGATE OF X₁₇₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 168}, {260, 266}

• Related Centers: X₁₇₄ (YFF CENTER OF CONGRUENCE), X₁ (INCENTER), X₁₆₈ (MITTENPUNKT OF EXCENTRAL TRIANGLE), X₂₆₀ (ISOGONAL CONJUGATE OF X₁₇₇), X₂₆₆ (ISOGONAL CONJUGATE OF X₁₈₈)

Trilinears: \(\cos A/2 : :\)

Barycentrics: \(\sin A \cos A/2 : :\)

Search Value (6, 9, 13): \(2.203419929256\)

▸ Alternate Coordinates5 forms

• Trilinears: \([a(b + c - a)]^{1/2} : :\)

• Trilinears: \(\sin A \csc A/2 : :\)

• Trilinears: \(\sin A' : :\), where J_aJ_bJ_c is the excentral triangle

• Trilinears: \(\sin(∠BIC) : :\)

• Trilinears: \((b + c - a) \sin A/2 : :\)

▸ Incident Central Lines3 lines

{1, 168}, {258, 289}, {260, 266}

▸ Functional Relations10 relations

• X₂₅₉ = isogonal conjugate of X₁₇₄

• X₂₅₉ = X_i-Ceva conjugate of X_j for these (i,j): (174, 266), (260, 55)

• X₂₅₉ = cevapoint of X₁ and X₅₀₃

• X₂₅₉ = crosspoint of X_i and X_j for these (i,j): (1, 258), (174, 188)

• X₂₅₉ = crosssum of X_i and X_j for these (i,j): (1, 173), (259, 266)

• X₂₅₉ = SS(A→J_a) of X₆, where J_aJ_bJ_c is the excentral triangle

• X₂₅₉ = trilinear square root of X₅₅

• X₂₅₉ = perspector of ABC and unary cofactor triangle of tangential mid-arc triangle

• X₂₅₉ = excentral-to-ABC trilinear image of X₉

• X₂₅₉ = intouch-to-ABC trilinear image of X₇