X₁₈₀₄

INVERSE MIMOSA TRANSFORM OF X₂₂₃

X₁₈₀₄ = X₉₂-isoconjugate of X₆₀₇

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

X₁₈₀₄ (INVERSE MIMOSA TRANSFORM OF X₂₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {7, 21}, {3, 77}

• Related Centers: X₁₈₅₇ (ZOSMA TRANSFORM OF X₂₂₃), X₇ (GERGONNE POINT), X₂₁ (SCHIFFLER POINT), X₃ (CIRCUMCENTER), X₇₇ (ISOGONAL CONJUGATE OF X₃₃)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X₂₂₃

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(1.782161008836\)

▸ Alternate Coordinates2 forms

• Trilinears: \((1 + \cos 2A)/(1 + \cos A) : (1 + \cos 2B)/(1 + \cos B) : (1 + \cos 2C)/(1 + \cos C)\) (M. Iliev, 4/12/07)

• Trilinears: \([\cos A \sec(A/2)]^{2} : [\cos B \sec(B/2)]^{2} : [\cos C \sec(C/2)]^{2}\) (M. Iliev, 4/12/07)

▸ Incident Central Lines13 lines

{3, 77}, {7, 21}, {20, 1440}, {36, 269}, {55, 1442}, {63, 268}, {69, 1809}, {198, 651}, {219, 1813}, {222, 1790}, {326, 1259}, {347, 934}, {573, 1461}

▸ Functional Relations3 relations

• X₁₈₀₄ = isogonal conjugate of X₁₈₅₇

• X₁₈₀₄ = X_i-Ceva conjugate of X_j for these (i,j): (348, 222), (1444, 77)

• X₁₈₀₄ = X₉₂-isoconjugate of X₆₀₇