X₂₃₁₆

X₂-ISOCONJUGATE OF X₁₃₁₉

X₂₃₁₆ is the perspector of the anticevian triangle of X₁₀₆ and the unary cofactor triangle of the intangents triangle, and also the perspector of ABC and the unary cofactor triangle of Gemini triangle 9. (Randy Hutson, November 30, 2018)

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

X₂₃₁₆ (X₂-ISOCONJUGATE OF X₁₃₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {6, 101}, {57, 88}

• Related Centers: X₃₉₁₁ (com[INTOUCH TRIANGLE))]), X₆ (SYMMEDIAN POINT), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₅₇ (ISOGONAL CONJUGATE OF X₉), X₈₈ (ISOGONAL CONJUGATE OF X₄₄)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₃₁₉

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

Search Value (6, 9, 13): \(0.542919983571\)

▸ Incident Central Lines16 lines

{6, 101}, {9, 644}, {19, 1743}, {36, 909}, {41, 2364}, {44, 517}, {57, 88}, {284, 2347}, {294, 1024}, {329, 1751}, {333, 645}, {527, 666}, {573, 2164}, {579, 1436}, {672, 901}, {1318, 2323}

▸ Functional Relations5 relations

• X₂₃₁₆ = isogonal conjugate of X₃₉₁₁

• X₂₃₁₆ = X_i-Ceva conjugate of X_j for these (i,j): (88, 106), (1318, 55)

• X₂₃₁₆ = cevapoint of X_i and X_j for these (i,j): (6, 2183), (41, 2361)

• X₂₃₁₆ = X_i-cross conjugate of X_j for these (i,j): (55, 1318), (654, 101), (2323, 284), (2342, 102)

• X₂₃₁₆ = crosssum of X_i and X_j for these (i,j): (44, 1319), (1149, 2183), (1635, 1647)