X₂₃₉₅

GIBERT-SIMSON TRANSFORM OF X₉₈

X₂₃₉₅ = X₆₈₅-Ceva conjugate of X₁₉₇₆

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

X₂₃₉₅ (GIBERT-SIMSON TRANSFORM OF X₉₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {98, 111}, {6, 523}

• Related Centers: X₂₄₂₁ (ISOGONAL CONJUGATE OF X₂₃₉₅), X₉₈ (TARRY POINT), X₁₁₁ (PARRY POINT), X₆ (SYMMEDIAN POINT), X₅₂₃ (ISOGONAL CONJUGATE OF X₁₁₀)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as given just before X₂₃₉₄

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

Search Value (6, 9, 13): \(-2.544418001681\)

▸ Alternate Coordinates1 form

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

X₂₃₉₅ lies on the cubic K010.

▸ Incident Central Lines10 lines

{2, 647}, {6, 523}, {25, 669}, {98, 111}, {263, 512}, {685, 2409}, {694, 804}, {880, 2396}, {892, 2407}, {1648, 2433}

▸ Functional Relations10 relations

• X₂₃₉₅ = isogonal conjugate of X₂₄₂₁

• X₂₃₉₅ = isotomic conjugate of X₂₃₉₆

• X₂₃₉₅ = anticomplement of isotomic conjugate of X₃₉₂₉₁

• X₂₃₉₅ = X₆₈₅-Ceva conjugate of X₁₉₇₆

• X₂₃₉₅ = cevapoint of X_i and X_j for these (i,j): (512, 2491), (523, 804), (878, 2422)

• X₂₃₉₅ = (X_i-cross conjugate of X_j for these (i,j): (878, 879), (2491, 512)

• X₂₃₉₅ = pole wrt polar circle of trilinear polar of X₈₇₇ (line X₂₃₂X₂₉₇)

• X₂₃₉₅ = polar conjugate of X₈₇₇

• X₂₃₉₅ = radical center of circumcircle and circles O(13,15) and O(14,16)

• X₂₃₉₅ = trilinear pole of line X₁₁₅X₅₁₂ (the Simson line of X₉₈, and the polar of X₈₇₇ wrt the polar circle)