X₂₂₇₀

X₂-ISOCONJUGATE OF X₉₆₃

X₂₂₇₀ = X₁₈₉-Ceva conjugate of X₁

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

X₂₂₇₀ (X₂-ISOCONJUGATE OF X₉₆₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 9}, {6, 57}

• Related Centers: X₁₈₉ (CYCLOCEVIAN CONJUGATE OF X₈), X₁ (INCENTER), X₄ (ORTHOCENTER), X₉ (MITTENPUNKT), X₆ (SYMMEDIAN POINT), X₅₇ (ISOGONAL CONJUGATE OF X₉)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₉₆₃

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(-2.475705968882\)

▸ Incident Central Lines21 lines

{1, 198}, {4, 9}, {6, 57}, {37, 1697}, {41, 1630}, {46, 1743}, {48, 1449}, {56, 1604}, {63, 391}, {84, 1741}, {165, 374}, {208, 1249}, {294, 2155}, {517, 2324}, {965, 1764}, {1394, 2199}, {1400, 2082}, {1420, 2178}, {1750, 1903}, {2173, 2261}, {2285, 2347}

▸ Functional Relations5 relations

• X₂₂₇₀ = X₁₈₉-Ceva conjugate of X₁

• X₂₂₇₀ = X₁₈₉-aleph conjugate of X₂₂₇₀

• X₂₂₇₀ = pole of Gergonne line wrt Bevan circle

• X₂₂₇₀ = homothetic center of 3rd extouch triangle and polar triangle of the Bevan circle

• X₂₂₇₀ = perspector of any pair of these triangles: {Danneels-Bevan, tangential of excentral, unary cofactor of intangents}