X₃₀₈₄

INTERSECTION OF LINES X₁X_2 AND X₃₇X_493

X₃₀₈₄ = isogonal conjugate of polar conjugate of X₄₆₇₄₅

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

X₃₀₈₄ (INTERSECTION OF LINES X₁X_2 AND X₃₇X_493) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 2}, {175, 329}

• Related Centers: X₆₀₆ (INTERSECTION OF LINES X), X₁ (INCENTER), X₂ (CENTROID), X₁₇₅ (ISOPERIMETRIC POINT), X₃₂₉ (ISOTOMIC CONJUGATE OF X₁₈₉)

Trilinears: \(1 - \csc A : :\)

Search Value (6, 9, 13): \(4.223179534196\)

▸ Alternate Coordinates1 form

• Trilinears: \(bc - S : ca - S : ab - S\)

▸ Incident Central Lines14 lines

{1, 2}, {11, 1592}, {12, 1591}, {33, 1585}, {34, 1586}, {35, 1599}, {36, 1600}, {37, 493}, {55, 1583}, {56, 1584}, {175, 329}, {394, 1335}, {1038, 1589}, {1040, 1590}

▸ Functional Relations4 relations

• X₃₀₈₄ = isogonal conjugate of polar conjugate of X₄₆₇₄₅

• X₃₀₈₄ = isotomic conjugate of isogonal conjugate of X₆₀₆

• X₃₀₈₄ = isotomic conjugate of polar conjugate of X₆₂₁₃

• X₃₀₈₄ = {X₁,X₂}-harmonic conjugate of X₃₀₈₃