X₁₈₀₇

INVERSE MIMOSA TRANSFORM OF X₄₈₄

X₁₈₀₇ = inverse-in-Feuerbach-hyperbola of X₁₄₁₁

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

X₁₈₀₇ (INVERSE MIMOSA TRANSFORM OF X₄₈₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 5}, {37, 101}

• Related Centers: X₁₈₇₀ (ZOSMA TRANSFORM OF X₄₈₄), X₁ (INCENTER), X₅ (NINE-POINT CENTER), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT))

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X₄₈₄

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

Search Value (6, 9, 13): \(2.379827829861\)

▸ Alternate Coordinates1 form

• Trilinears: \(1/(2 - \sec A) : 1/(2 - \sec B) : 1/(2 - \sec C)\)

▸ Incident Central Lines16 lines

{1, 5}, {3, 201}, {29, 1897}, {37, 101}, {72, 283}, {73, 265}, {77, 1060}, {78, 1062}, {102, 517}, {296, 916}, {912, 1795}, {942, 951}, {945, 1482}, {947, 1385}, {976, 1036}, {999, 1037}

▸ Functional Relations5 relations

• X₁₈₀₇ = isogonal conjugate of X₁₈₇₀

• X₁₈₀₇ = crosssum of X_i and X_j for these (i,j): (1, 1718), (1464, 1835)

• X₁₈₀₇ = inverse-in-Feuerbach-hyperbola of X₁₄₁₁

• X₁₈₀₇ = {X₁,X₈₀}-harmonic conjugate of X₁₄₁₁

• X₁₈₀₇ = inverse-in-circumconic-centered-at-X₁ of X₈₀