X₃₉₃₉

X₁₀₈₆com[INVERSE(n(INTOUCH TRIANGLE))]

X₃₉₃₉ = trilinear pole of line X₄₁X₅₅

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

X₃₉₃₉ (X₁₀₈₆com[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: {100, 109}, {9, 294}

• Related Centers: X₁ (INCENTER), X₃₆₇₆ (com(INTOUCH TRIANGLE)), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₁₀₉ (Ψ(INCENTER, CIRCUMCENTER)), X₉ (MITTENPUNKT), X₂₉₄ (ISOGONAL CONJUGATE OF X₂₄₁)

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

Search Value (6, 9, 13): \(8.058660028871\)

▸ Incident Central Lines24 lines

{3, 2810}, {9, 294}, {31, 678}, {40, 2835}, {55, 2316}, {59, 677}, {100, 109}, {101, 692}, {190, 522}, {200, 212}, {210, 2328}, {219, 480}, {284, 2311}, {573, 2876}, {643, 645}, {1018, 1783}, {1026, 1332}, {1461, 2283}, {1471, 3243}, {1724, 3189}, {1743, 3174}, {2209, 3169}, {2323, 2340}, {2361, 3689}

▸ Functional Relations5 relations

• X₃₉₃₉ = isogonal conjugate of X₃₆₇₆

• X₃₉₃₉ = trilinear pole of line X₄₁X₅₅

• X₃₉₃₉ = crossdifference of every pair of points on line X₁₀₈₆X₁₃₅₈

• X₃₉₃₉ = barycentric product of circumcircle intercepts of line X₈X₉

• X₃₉₃₉ = perspector of anticevian triangle of X₁₀₁ and unary cofactor triangle of intangents triangle