X₁₉₆₀

BICENTRIC SUM OF PU(25)

X₁₉₆₀ = bicentric sum of PU(25)

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

X₁₉₆₀ (BICENTRIC SUM OF PU(25)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {187, 237}, {1, 659}

• Related Centers: X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X), X₂₃₇ (-LINE CONJUGATE OF X₂), X₁ (INCENTER), X₆₅₉ (CROSSDIFFERENCE OF X₁ AND X₃₉)

Trilinears: \(a(b - c)(2a - b - c) : :\)

Search Value (6, 9, 13): \(-2.414726442081\)

▸ Incident Central Lines8 lines

{1, 659}, {101, 692}, {187, 237}, {214, 900}, {292, 875}, {660, 898}, {678, 1635}, {884, 1438}

▸ Functional Relations12 relations

• X₁₉₆₀ = midpoint of X_i and X_j for these (i,j): (1, 659), (663, 667), (1635, 3251)

• X₁₉₆₀ = isogonal conjugate of X₄₅₅₅

• X₁₉₆₀ = complement of anticomplementary conjugate of X₃₉₃₄₉

• X₁₉₆₀ = X_i-Ceva conjugate of X_j for these (i,j): (101, 1017), (106, 1015), (901, 6), (1319, 2087)

• X₁₉₆₀ = crosspoint of X_i and X_j for these (i,j): (6, 901), (101, 106)

• X₁₉₆₀ = crosssum of X_i and X_j for these (i,j): (2, 900), 514,519)

• X₁₉₆₀ = bicentric sum of PU(25)

• X₁₉₆₀ = PU(25)-harmonic conjugate of X₁₀₁₅

• X₁₉₆₀ = bicentric difference of PU(99)

• X₁₉₆₀ = PU(99)-harmonic conjugate of X₁₀₁₇

• X₁₉₆₀ = polar conjugate of isotomic conjugate of X₂₂₀₈₆

• X₁₉₆₀ = crossdifference of every pair of points on line X₂X₄₅

Notes

X₁₉₆₀ is the center of the circle V(X₁₀₁) = {{15,16,101,106}}; see the preamble to X₆₁₃₇. (Randy Hutson, December 26, 2015)