X₁₁₆₄

POINT ALTAIR

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

X₁₁₆₄ (POINT ALTAIR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {468, 1165}

• Related Centers: X₄₆₈ (-LINE CONJUGATE OF X₃), X₁₁₆₅ (POINT ALTAIS)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (\operatorname{area} + a^{2})(2 \operatorname{area} - b^{2} - c^{2})/[a(b^{2} + c^{2} - a^{2})]\)

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

Search Value (6, 9, 13): \(-6.502445573938\)

▸ Incident Central Lines1 line

{468, 1165}