X₁₅₀₄

INSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES

X₁₅₀₄ is the insimilicenter of moses and 2nd Lemoine circles.

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

X₁₅₀₄ (INSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {2, 588}

• Related Centers: X₁₃₀₆ (COLLINGS TRANSFORM OF X₆₃₉), X₅₁₂ (ISOGONAL CONJUGATE OF X₉₉), X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₂ (CENTROID), X₅₈₈ (1st KENMOTU-VAN LAMOEN POINT)

Trilinears: \(a[b^{2} + c^{2} + 4(\operatorname{area} ABC)]\)

Search Value (6, 9, 13): \(1.350903836387\)

▸ Alternate Coordinates2 forms

• Trilinears: \(2 \sin A \sin \omega + \sin(A + \omega ) : :\) (Peter J. C. Moses, 9/12/03)

• Trilinears: \(\cos A + (\sin A)(2 + \cot \omega ) : :\) (Peter J. C. Moses, 9/12/03)

▸ Linear Combinations1 combination

• X₁₅₀₄ = \(\sin(2\omega )\) X₆ + X₃₉

▸ Incident Central Lines9 lines

{2, 588}, {3, 6}, {115, 485}, {394, 493}, {486, 1508}, {491, 626}, {590, 639}, {1015, 1124}, {1335, 1500}

▸ Functional Relations6 relations

• X₁₅₀₄ = internal center of similitude of the Moses circle and the 2nd Lemoine circle. [See X₁₅₀₀; Peter J. C. Moses, 6/2/03]

• X₁₅₀₄ = X₁₃₀₆-Ceva conjugate of X₅₁₂

• X₁₅₀₄ = crosspoint of X₆ and X₄₉₃

• X₁₅₀₄ = isogonal conjugate of the polar conjugate of X₃₂₅₈₈

• X₁₅₀₄ = {X₆,X₃₉}-harmonic conjugate of X₁₅₀₅

• X₁₅₀₄ = intersection of tangents to hyperbola {A, B, C,X₂,X₆} at X₆ and X₄₉₃