X₄₄₆

CROSSPOINT OF X₉₈ AND X₅₁₁

X₄₄₆ is the crosspoint of X₉₈ and X₅₁₁.

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

X₄₄₆ (CROSSPOINT OF X₉₈ AND X₅₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line)

• Related Centers: X₉₈ (TARRY POINT), X₅₁₁ (ISOGONAL CONJUGATE OF X₉₈), X₂ (CENTROID), X₃ (CIRCUMCENTER)

Trilinears: \(u(v^{2} + w^{2}) : v(w^{2} + u^{2}) : w(u^{2} + v^{2})\), where \(u : v : w\) = X₉₈; e.g., \(u(A,B,C) = \sec(A + \omega )\)

Barycentrics: \(au(v^{2} + w^{2}) : bv(w^{2} + u^{2}) : cw(u^{2} + v^{2})\)

Search Value (6, 9, 13): \(28.482023066739\)

▸ Incident Central Lines1 line

{2, 3}

▸ Functional Relations2 relations

• X₄₄₆ = crosspoint of X₉₈ and X₅₁₁

• X₄₄₆ = crosssum of X_i and X_j for these (i,j): (98, 511), (287, 385)

Notes

As a point on the Euler line, X₄₄₆ has Shinagawa coefficients \(((E + F)^{3}F - (E + F)(E - 2F)S^{2} + S^{4}, (E - F)(E + F)^{3} - 2(E + F)^{2}S^{2} - S^{4})\).