X₁₈₀₂

INVERSE MIMOSA TRANSFORM OF X₁₇₀

X₁₈₀₂ = X₉₂-isoconjugate of X₂₆₉

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

X₁₈₀₂ (INVERSE MIMOSA TRANSFORM OF X₁₇₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 48}, {41, 55}

• Related Centers: X₁₈₄₇ (ZOSMA TRANSFORM OF X₁₇₀), X₃ (CIRCUMCENTER), X₄₈ (CROSSPOINT OF X₁ AND X₆₃), X₄₁ (-CEVA CONJUGATE OF X₃₁), X₅₅ (INSIMILICENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X₁₇₀

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

Search Value (6, 9, 13): \(4.572042641973\)

▸ Alternate Coordinates2 forms

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

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \cos A \cot(A/2) \cos^{2}(A/2)\) (P. Moses, 12/6/11)

▸ Incident Central Lines7 lines

{3, 48}, {6, 939}, {9, 943}, {40, 101}, {41, 55}, {63, 1803}, {255, 906}

▸ Functional Relations5 relations

• X₁₈₀₂ = isogonal conjugate of X₁₈₄₇

• X₁₈₀₂ = X_i-Ceva conjugate of X_j for these (i,j): (200, 1253), (219, 212)

• X₁₈₀₂ = crosspoint of X_i and X_j for these (i,j): (219, 1260), (906, 1110)

• X₁₈₀₂ = crosssum of X_i and X_j for these (i,j): (269, 1435), (278, 1119)

• X₁₈₀₂ = X₉₂-isoconjugate of X₂₆₉