X₂₉₇₂

6th MACBEATH POINT

X₂₉₇₂ = crossdifference of every pair of points on line X₁₀₇X₁₁₂

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

X₂₉₇₂ (6th MACBEATH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 74}, {122, 125}

• Related Centers: X₃ (CIRCUMCENTER), X₇₄ (ISOGONAL CONJUGATE OF EULER INFINITY POINT), X₁₂₂ (-OF-MEDIAL-TRIANGLE), X₁₂₅ (CENTER OF JERABEK HYPERBOLA)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = [bc(b^{2} - c^{2})]^{2}\cos^{3} A\)

Barycentrics: \((\csc 2A) (\sec^{2} B - \sec^{2} C)^{2} : :\)

Search Value (6, 9, 13): \(3.979351338958\)

▸ Incident Central Lines10 lines

{2, 1972}, {3, 74}, {25, 1073}, {69, 1942}, {122, 125}, {127, 136}, {394, 426}, {511, 852}, {1368, 2974}, {1624, 2781}

▸ Functional Relations11 relations

• X₂₉₇₂ = reflection of X₃₄₃₃₄ in X₅

• X₂₉₇₂ = isogonal conjugate of X₃₂₂₃₀

• X₂₉₇₂ = complement of X₃₅₃₆₀

• X₂₉₇₂ = X_i-Ceva conjugate of X_j for these (i,j): (3, 520), (264, 525), (1073, 647)

• X₂₉₇₂ = crosspoint of X_i and X_j for these (i,j): (3, 520), (64, 523), (264, 525)

• X₂₉₇₂ = crosssum of X_i and X_j for these (i,j): (4, 107), (20, 110), (112, 184)

• X₂₉₇₂ = crossdifference of every pair of points on line X₁₀₇X₁₁₂

• X₂₉₇₂ = polar conjugate of X₃₄₅₃₈

• X₂₉₇₂ = MacBeath-inconic-antipode of X₃₄₃₃₄

• X₂₉₇₂ = center of conic {{A, B, C,X₃,X₅}}

• X₂₉₇₂ = X₉₂-isoconjugate of X₂₃₉₆₄