X₂₄₆₀

INVERSE-IN-CIRCUMCIRCLE OF X₃₇₂

X₂₄₆₀ = reflection of X₂₄₅₉ in X₁₈₇

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

X₂₄₆₀ (INVERSE-IN-CIRCUMCIRCLE OF X₃₇₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2459, 187}

• Related Centers: X₂₄₅₉ (INVERSE-IN-CIRCUMCIRCLE OF X₃₇₁), 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): \(1.013147874324\)

▸ Incident Central Lines2 lines

{3, 6}, {486, 489}

▸ Functional Relations7 relations

• X₂₄₆₀ = reflection of X₂₄₅₉ in X₁₈₇

• X₂₄₆₀ = anticomplement of X₃₂₄₃₅

• X₂₄₆₀ = crossdifference of every pair of points on line X₅₂₃X₆₁₅

• X₂₄₆₀ = perspector of ABC and the reflection of the Lucas(-1) tangents triangle in the Lemoine axis

• X₂₄₆₀ =Lucas-radical-circle-inverse of X₃₇₁

• X₂₄₆₀ = X₂₄₆₀-of-2nd-Brocard-triangle

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