X₁₇₈₃

MIMOSA TRANSFORM OF X₁₂₆₂

X₁₇₈₃ = trilinear pole of line X₁₉X₂₅ (the tangent to hyperbola {{A, B, C,X₄,X₁₉}} at X₁₉)

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

X₁₇₈₃ (MIMOSA TRANSFORM OF X₁₂₆₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {101, 108}, {100, 112}

• Related Centers: X₉₀₅ (POINT ACHERNAR), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₁₀₈ (Ψ(CIRCUMCENTER, INCENTER)), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT))

Trilinears: \((\tan A)/(b - c) : (\tan B)/(c - a) : (\tan C)/(a - b)\)

Barycentrics: \(a(\tan A)/(b - c) : b(\tan B)/(c - a) : c(\tan C)/(a - b)\)

Search Value (6, 9, 13): \(-0.637775688478\)

▸ Incident Central Lines19 lines

{4, 218}, {6, 281}, {19, 1743}, {28, 291}, {80, 1172}, {100, 112}, {101, 108}, {150, 1814}, {200, 204}, {219, 1249}, {240, 1757}, {644, 648}, {650, 1415}, {651, 653}, {899, 1430}, {905, 934}, {1103, 1712}, {1718, 1723}, {1785, 1886}

▸ Functional Relations17 relations

• X₁₇₈₃ = isogonal conjugate of X₉₀₅

• X₁₇₈₃ = isotomic conjugate of X₁₅₄₁₃

• X₁₇₈₃ = trilinear pole of line X₁₉X₂₅ (the tangent to hyperbola {{A, B, C,X₄,X₁₉}} at X₁₉)

• X₁₇₈₃ = pole wrt polar circle of trilinear polar of X₆₉₃ (line X₉₁₈X₁₀₈₆)

• X₁₇₈₃ = polar conjugate of X₆₉₃

• X₁₇₈₃ = crossdifference of every pair of points on line X₁₃₆₄X₃₂₇₀

• X₁₇₈₃ = perspector of anticevian triangle of X₁₀₈ and unary cofactor triangle of intangents triangle

• X₁₇₈₃ = barycentric product of circumcircle intercepts of line X₄X₈

• X₁₇₈₃ = barycentric product X₄*X₁₀₀

• X₁₇₈₃ = X_i-Ceva conjugate of X_j for these (i,j): (648, 1897), (653, 108)

• X₁₇₈₃ = cevapoint of X_i and X_j for these (i,j): (1, 1734), (6, 650), (513, 614)

• X₁₇₈₃ = crosspoint of X_i and X_j for these (i,j): (162, 648), (653, 1897)

• X₁₇₈₃ = crosssum of X_i and X_j for these (i,j): (647, 656), (652, 1459), (513, 614)

• X₁₇₈₃ = X_i-aleph conjugate of X_j for these (i,j): (108, 1707), (651, 610), (653, 19)

• X₁₇₈₃ = X₉₂-isoconjugate of X₂₃₂₂₄

• X₁₇₈₃ = trilinear product X₄*X₁₀₁

• X₁₇₈₃ = trilinear product of circumcircle intercepts of line X₄X₉