X₉₉₇

MIDPOINT OF X₁ AND X₂₀₀

X₉₉₇ is the midpoint of X₁ and X₂₀₀.

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

X₉₉₇ (MIDPOINT OF X₁ AND X₂₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 200}

• Related Centers: X₁ (INCENTER), X₂₀₀ (-CEVA CONJUGATE OF X₉)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{3} - a^{2}(b + c) - a(b - c)^{2} + (b + c)(b^{2} + c^{2})\)

Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)

Search Value (6, 9, 13): \(3.280068120442\)

▸ Incident Central Lines14 lines

{1, 2}, {3, 960}, {9, 48}, {21, 90}, {34, 860}, {36, 63}, {46, 404}, {55, 392}, {56, 72}, {57, 758}, {65, 474}, {141, 1060}, {210, 956}, {518, 999}

▸ Functional Relations2 relations

• X₉₉₇ = midpoint of X_i and X_j for these (i,j): (1, 200), (3421, 3476)

• X₉₉₇ = isogonal conjugate of X₉₉₈