X₉₂₂

POINT ALBALI

X₉₂₂ = trilinear product of PU(107)

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

X₉₂₂ (POINT ALBALI) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {31, 48}, {667, 788}

• Related Centers: X₈₉₆ (INTERSECTION OF LINES X), X₃₁ (2nd POWER POINT), X₄₈ (CROSSPOINT OF X₁ AND X₆₃), X₆₆₇ (CROSSDIFFERENCE OF X₂ AND X₃₇), X₇₈₈ (ODD (- 3, 0) INFINITY POINT)

Trilinears: \(a^{2}(b^{2} + c^{2} - 2a^{2})\) (M. Iliev, 5/13/07)

Search Value (6, 9, 13): \(-0.729495489993\)

▸ Incident Central Lines2 lines

{31, 48}, {667, 788}

▸ Functional Relations6 relations

• X₉₂₂ = isogonal conjugate of isotomic conjugate of X₈₉₆

• X₉₂₂ = isogonal conjugate of complement of anticomplementary conjugate of X₂₁₂₉₈

• X₉₂₂ = isogonal conjugate of anticomplement of complementary conjugate of X₂₁₂₅₆

• X₉₂₂ = complement of X₂₁₂₉₈

• X₉₂₂ = anticomplement of X₂₁₂₅₆

• X₉₂₂ = trilinear product of PU(107)