X₃₁₆₁

X₂-CEVA CONJUGATE OF X₈

X₃₁₆₁ = perspector of triangle ABC and the tangential triangle of the conic that passes through A, B, C and has center X₈

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

X₃₁₆₁ (X₂-CEVA CONJUGATE OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 9}, {190, 344}

• Related Centers: X₂ (CENTROID), X₈ (NAGEL POINT), X₉ (MITTENPUNKT), X₁₉₀ (YFF PARABOLIC POINT), X₃₄₄ (ISOTOMIC CONJUGATE OF X₂₇₇)

Trilinears: \(bc(b + c - a)(b + c - 3a)\) (M. Iliev, 5/13/07)

Search Value (6, 9, 13): \(-7.888106377466\)

▸ Incident Central Lines11 lines

{2, 2415}, {6, 644}, {8, 9}, {37, 2275}, {45, 1213}, {145, 1743}, {190, 344}, {268, 1809}, {329, 440}, {355, 537}, {404, 1696}

▸ Functional Relations8 relations

• X₃₁₆₁ = perspector of triangle ABC and the tangential triangle of the conic that passes through A, B, C and has center X₈

• X₃₁₆₁ = X_i-Ceva conjugate of X_j for these (i,j): (2, 8), (1222, 200)

• X₃₁₆₁ = X₃₁₅₈-cross conjugate of X₁₄₅

• X₃₁₆₁ = crosspoint of X₂ and X₁₄₅

• X₃₁₆₁ = crosssum of X₆₄₉ and X₁₃₅₇

• X₃₁₆₁ = center of circumconic that is locus of trilinear poles of lines passing through X₈; this conic is the isotomic conjugate of the Gergonne line.

• X₃₁₆₁ = complement of X₄₃₇₃

• X₃₁₆₁ = anticomplement of X₄₈₅₉