X₂₄₅₆

INVERSE-IN-1st-LEMOINE CIRCLE OF X₃

X₂₄₅₆ = harmonic center of circumcircle and 8th Lozada circle

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

X₂₄₅₆ (INVERSE-IN-1st-LEMOINE CIRCLE OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {98, 325}

• Related Centers: X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₉₈ (TARRY POINT), X₃₂₅ (-HIRST INVERSE OF X₆₉)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = e^{2}\cos(A - \omega ) + \cos(A + \omega )\), \(e = (1 - 4 \sin^{2} \omega )^{1/2}\)

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

Search Value (6, 9, 13): \(8.671557715968\)

▸ Incident Central Lines2 lines

{3, 6}, {98, 325}

▸ Functional Relations3 relations

• X₂₄₅₆ = reflection of X_i in X_j for these (i,j): (1351, 1570), (1691, 182), (2080, 1691)

• X₂₄₅₆ = {X₁₆₈₇,X₁₆₈₈}-harmonic conjugate of X₁₆₉₂

• X₂₄₅₆ = harmonic center of circumcircle and 8th Lozada circle