X₁₉₂₄

BICENTRIC DIFFERENCE OF PU(13)

X₁₉₂₄ = trilinear product of PU(91)

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

X₁₉₂₄ (BICENTRIC DIFFERENCE OF PU(13)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {667, 788}, {661, 830}

• Related Centers: X₆₆₇ (CROSSDIFFERENCE OF X₂ AND X₃₇), X₇₈₈ (ODD (- 3, 0) INFINITY POINT), X₆₆₁ (CROSSDIFFERENCE OF X₁ AND X₂₁), X₈₃₀ (ODD (1, 3) INFINITY POINT)

Trilinears: \(a^{4}(b^{2} - c^{2}) : b^{4}(c^{2} - a^{2}) : c^{4}(a^{2} - b^{2})\)

Barycentrics: \(a^{5}(b^{2} - c^{2}) : b^{5}(c^{2} - a^{2}) : c^{5}(a^{2} - b^{2})\)

Search Value (6, 9, 13): \(0.565862400123\)

▸ Incident Central Lines3 lines

{661, 830}, {667, 788}, {681, 1612}

▸ Functional Relations6 relations

• X₁₉₂₄ = X_i-Ceva conjugate of X_j for these (i,j): (163, 1923), (662, 31), (1919, 669)

• X₁₉₂₄ = crosspoint of X_i and X_j for these (i,j): (31, 662), (1919, 1980)

• X₁₉₂₄ = crosssum of X_i and X_j for these (i,j): (75, 661), (1577, 1930)

• X₁₉₂₄ = isogonal conjugate of X₄₆₀₂

• X₁₉₂₄ = PU(13)-harmonic conjugate of X₁₉₂₃

• X₁₉₂₄ = trilinear product of PU(91)