X₂₄₅₉

INVERSE-IN-CIRCUMCIRCLE OF X₃₇₁

X₂₄₅₉ = reflection of X₂₄₆₀ in X₁₈₇

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

X₂₄₅₉ (INVERSE-IN-CIRCUMCIRCLE OF X₃₇₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2460, 187}

• Related Centers: X₂₄₆₀ (INVERSE-IN-CIRCUMCIRCLE OF X₃₇₂), X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \cos(A + \omega ) - \cos \omega \sin A + 3 \cos A \sin \omega\)

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

Search Value (6, 9, 13): \(-4.694915349508\)

▸ Incident Central Lines2 lines

{3, 6}, {485, 490}

▸ Functional Relations7 relations

• X₂₄₅₉ = reflection of X₂₄₆₀ in X₁₈₇

• X₂₄₅₉ = anticomplement of X₃₂₄₃₂

• X₂₄₅₉ = perspector of ABC and the reflection of the Lucas tangents triangle in the Lemoine axis

• X₂₄₅₉ = inverse-in-Lucas(-1)-radical-circle of X₃₇₂

• X₂₄₅₉ = X₂₄₅₉ of 2nd Brocard triangle

• X₂₄₅₉ = crossdifference of every pair of points on line X₅₂₃X₅₉₀

• X₂₄₅₉ = Brocard axis intercept, other than X₂₄₆₀, of circle with segment PU(2) as diameter