X₈₉₉

INTERSECTION OF LINES X₁X_2 AND X₆X_750

X₈₉₉ = crossdifference of every pair of points on line X₁X₆₄₉

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

X₈₉₉ (INTERSECTION OF LINES X₁X_2 AND X₆X_750) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 2}, {38, 210}

• Related Centers: X₁ (INCENTER), X₂ (CENTROID), X₃₈ (CROSSPOINT OF X₁ AND X₇₅), X₂₁₀ (-CEVA CONJUGATE OF X₃₇)

Trilinears: \(1/b + 1/c - 2/a : 1/c + 1/a - 2/b : 1/a + 1/b - 2/c\) (Joe Goggins, 2002)

Barycentrics: \(a(1/b + 1/c - 2/a) : b(1/c + 1/a - 2/b) : c(1/a + 1/b - 2/c)\)

Search Value (6, 9, 13): \(-7.381530738546\)

▸ Incident Central Lines8 lines

{1, 2}, {6, 750}, {38, 210}, {44, 513}, {55, 748}, {88, 291}, {100, 238}, {244, 518}

▸ Functional Relations11 relations

• X₈₉₉ = isogonal conjugate of X₃₇₁₂₉

• X₈₉₉ = isotomic conjugate of X₃₁₀₀₂

• X₈₉₉ = complement of X₂₉₈₂₄

• X₈₉₉ = anticomplement of X₄₈₇₁

• X₈₉₉ = cevapoint of X_i and X_j for these {i,j}: {891, 19945}, {1646, 14404}

• X₈₉₉ = trilinear pole of line X₈₉₁X₃₇₆₈

• X₈₉₉ = crosspoint of X_i and X_j for these {i,j}: {1, 37129}, {4607, 7035}

• X₈₉₉ = crosssum of X_i and X_j for these {i,j}: {1, 899}, {513, 16507}, {3248, 3768}

• X₈₉₉ = crossdifference of every pair of points on line X₁X₆₄₉

• X₈₉₉ = bicentric sum of PU(58)

• X₈₉₉ = PU(58)-harmonic conjugate of X₆₄₉