X₁₇₅₇

MIMOSA TRANSFORM OF X₂₉₅

X₁₇₅₇ = X₂₉₁-Ceva conjugate of X₁

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

X₁₇₅₇ (MIMOSA TRANSFORM OF X₂₉₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 6}, {43, 63}

• Related Centers: X₁₉₂₉ (ISOGONAL CONJUGATE OF X₁₇₅₇), X₁ (INCENTER), X₆ (SYMMEDIAN POINT), X₄₃ (-CEVA CONJUGATE OF X₁), X₆₃ (ISOGONAL CONJUGATE OF X₁₉)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c)^{2} - (a + b)(a + c)\)

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

Search Value (6, 9, 13): \(-9.091118740053\)

▸ Incident Central Lines22 lines

{1, 6}, {10, 894}, {42, 846}, {43, 63}, {57, 1463}, {81, 756}, {100, 896}, {171, 210}, {190, 740}, {191, 1045}, {200, 1707}, {209, 1762}, {239, 726}, {240, 1783}, {314, 1089}, {320, 1698}, {333, 1215}, {484, 513}, {527, 1738}, {672, 1282}, {765, 1110}, {899, 1054}

▸ Functional Relations11 relations

• X₁₇₅₇ = reflection of X_i in X_j for these (i,j): (1, 238), (238, 44)

• X₁₇₅₇ = isogonal conjugate of X₁₉₂₉

• X₁₇₅₈ = X₂-Ceva conjugate of X₃₉₀₅₅

• X₁₇₅₇ = X₂₉₁-Ceva conjugate of X₁

• X₁₇₅₇ = crosspoint of X₆₆₀ and X₇₆₅

• X₁₇₅₇ = crosssum of X_i and X_j for these (i,j): (244, 659), (1931, 1963)

• X₁₇₅₇ = X_i-aleph conjugate of X_j for these (i,j): (291, 1757), (660, 1026)

• X₁₇₅₇ = crossdifference of PU(31)

• X₁₇₅₇ = perspector of conic {A, B, C,X₁₀₀,PU(32)}

• X₁₇₅₇ = intersection of trilinear polars of X₁₀₀, P(32), and U(32)

• X₁₇₅₇ = inverse-in-circumconic-centered-at-X₉ of X₃₇