X₃₉₂₀

X₃₇₄₅com[INVERSE(n(INTOUCH TRIANGLE))]

X₃₉₂₀ = complement of X₃₃₀₉₀

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

X₃₉₂₀ (X₃₇₄₅com[INVERSE(n(INTOUCH TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Circle: Incircle (incircle) — Inscribed circle tangent to sidelines at T_a, T_b, T_c; centered at X₁ INCENTER

• Central Lines: {1, 2}, {22, 55}

• Related Centers: X₁ (INCENTER), X₂ (CENTROID), X₂₂ (EXETER POINT), X₅₅ (INSIMILICENTER)

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(a^{2} + b^{2} + c^{2} + bc)\)

Search Value (6, 9, 13): \(1.885845483559\)

▸ Incident Central Lines39 lines

{1, 2}, {6, 3681}, {22, 55}, {23, 3743}, {25, 3295}, {31, 984}, {33, 390}, {37, 82}, {38, 171}, {81, 518}, {86, 3263}, {100, 3666}, {105, 1255}, {172, 1627}, {210, 1386}, {238, 756}, {388, 1370}, {427, 495}, {611, 1993}, {750, 982}, {846, 902}, {940, 3242}, {968, 3749}, {1038, 3600}, {1056, 1060}, {1150, 3769}, {1172, 2346}, {1180, 2276}, {1194, 1500}, {1203, 3678}, {1469, 2979}, {1757, 2308}, {1921, 3112}, {1962, 3722}, {1995, 3303}, {3056, 3060}, {3290, 3723}, {3306, 3677}, {3315, 3742}

▸ Functional Relations1 relation

• X₃₉₂₀ = complement of X₃₃₀₉₀