X₅₅₁

MIDPOINT OF X₁ AND X₂

X₅₅₁ is the midpoint of X₁ and X₂.

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

X₅₅₁ (MIDPOINT OF X₁ AND X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 2}

• Related Centers: X₁ (INCENTER), X₂ (CENTROID)

Trilinears: \((4a + b + c)/a : (4b + c + a)/b : (4c + a + b)/c\)

Barycentrics: \(4a + b + c : 4b + c + a : 4c + a + b\)

Search Value (6, 9, 13): \(2.159838650973\)

▸ Alternate Coordinates1 form

• Trilinears: \(3 r + 2 R \sin B \sin C :\)

▸ Linear Combinations1 combination

• X₅₅₁ = X₁ + X₂ = \(2\) X₈ - \(5\) X₁₀

▸ Incident Central Lines15 lines

{1, 2}, {30, 946}, {37, 537}, {56, 553}, {86, 99}, {142, 214}, {226, 535}, {354, 392}, {376, 516}, {381, 515}, {514, 676}, {517, 549}, {518, 597}, {527, 993}, {547, 952}

▸ Functional Relations7 relations

• X₅₅₁ = midpoint of X_i and X_j for these (i,j): (2, 1125), (10, 2)

• X₅₅₁ = reflection of X_i in X_j for these (i,j): (14, 619), (148, 13), (616, 99), (622, 299)

• X₅₅₁ = complement of X₃₆₇₉

• X₅₅₁ = anticomplement of X₃₈₂₈

• X₅₅₁ = isotomic conjugate of isogonal conjugate of X₂₁₇₄₇

• X₅₅₁ = complementary conjugate of X₂₁₂₅₁

• X₅₅₁ = polar conjugate of isogonal conjugate of X₂₂₃₅₇

Notes

(Antreas Hatzipolakis, 1/24/00, Hyacinthos #223)