X₂₉₀

ISOGONAL CONJUGATE OF X₂₃₇

X₂₉₀ is the isogonal conjugate of X₂₃₇.

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

X₂₉₀ (ISOGONAL CONJUGATE OF X₂₃₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 76}, {71, 190}

• Related Centers: X₂₃₇ (-LINE CONJUGATE OF X₂), X₃ (CIRCUMCENTER), X₇₆ (3rd BROCARD POINT), X₇₁ (ISOGONAL CONJUGATE OF X₂₇), X₁₉₀ (YFF PARABOLIC POINT)

Trilinears: \(\csc^{2} A \sec(A + \omega ) : :\)

Barycentrics: \(\csc A \sec(A + \omega ) : :\)

Search Value (6, 9, 13): \(5.597957171766\)

▸ Alternate Coordinates1 form

• Barycentrics: \(b^{2} c^{2}/(b^{4} + c^{4} - a^{2} b^{2} - a^{2} c^{2}) : :\)

X₂₉₀ lies on the Steiner circumellipse.

▸ Incident Central Lines15 lines

{2, 327}, {3, 76}, {6, 264}, {54, 276}, {66, 317}, {67, 340}, {68, 315}, {69, 670}, {71, 190}, {72, 668}, {73, 336}, {248, 385}, {265, 316}, {308, 311}, {892, 895}

▸ Functional Relations18 relations

• X₂₉₀ = isogonal conjugate of X₂₃₇

• X₂₉₀ = isotomic conjugate of X₅₁₁

• X₂₉₀ = complement of X₃₉₃₅₅

• X₂₉₀ = X₂-Ceva conjugate of X₃₉₀₅₈

• X₂₉₀ = cevapoint of X_i and X_j for these (i,j): (2, 511), (98, 287)

• X₂₉₀ = X_i-cross conjugate of X_j for these (i,j): (385, 308), (401, 276), (511, 2)

• X₂₉₀ = point of intersection, other than A, B, C, of Steiner circumellipse and Jerabek hyperbola

• X₂₉₀ = trilinear pole of line X₂X₆₄₇ (the line through the polar conjugates of PU(39))

• X₂₉₀ = pole wrt polar circle of trilinear polar of X₂₃₂

• X₂₉₀ = X₄₈-isoconjugate (polar conjugate) of X₂₃₂

• X₂₉₀ = X₆-isoconjugate of X₁₇₅₅

• X₂₉₀ = crossdifference of PU(89)

• X₂₉₀ = areal center of cevian triangles of PU(37)

• X₂₉₀ = areal center of cevian triangles of PU(45)

• X₂₉₀ = perspector of hyperbola {A, B, C,X₂₂₄₅₆,PU(177)}}

• X₂₉₀ = Steiner-circumellipse-X₃-antipode of X₉₉

• X₂₉₀ = Steiner-circumellipse-X₄-antipode of X₆₅₂₈

• X₂₉₀ = Steiner-circumellipse-X₆-antipode of X₆₄₈