X₁₆₆₄

INVERSE-IN-BROCARD-CIRCLE OF X₁₆₆₂

X₁₆₆₄ = reflection of X₁₆₆₅ in X₁₈₂

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

X₁₆₆₄ (INVERSE-IN-BROCARD-CIRCLE OF X₁₆₆₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1665, 182}

• Related Centers: X₁₆₆₅ (INVERSE-IN-BROCARD-CIRCLE OF X₁₆₆₃), X₁₈₂ (MIDPOINT OF BROCARD DIAMETER)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = e \cos(A + \omega ) + \cos(A - \omega )\)

Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)

Search Value (6, 9, 13): \(6.139381782233\)

▸ Incident Central Lines1 line

{3, 6}

▸ Functional Relations2 relations

• X₁₆₆₄ = reflection of X₁₆₆₅ in X₁₈₂

• X₁₆₆₄ = inverse-in-Brocard-circle of X₁₆₆₂