X₃₉₅₂

X₂₄₄com[INVERSE(n(INCENTRAL TRIANGLE))]

X₃₉₅₂ = anticomplement of X₂₄₄

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

X₃₉₅₂ (X₂₄₄com[INVERSE(n(INCENTRAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 38}, {8, 80}

• Related Centers: X₃₇₃₃ (com(TANGENTIAL TRIANGLE)), X₂ (CENTROID), X₃₈ (CROSSPOINT OF X₁ AND X₇₅), X₈ (NAGEL POINT), X₈₀ (REFLECTION OF INCENTER IN FEUERBACH POINT)

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

Search Value (6, 9, 13): \(5.572332028118\)

▸ Incident Central Lines20 lines

{2, 38}, {8, 80}, {10, 3120}, {37, 3121}, {72, 3701}, {100, 190}, {101, 835}, {110, 645}, {192, 872}, {210, 321}, {312, 3681}, {329, 2835}, {643, 765}, {644, 1783}, {660, 799}, {668, 891}, {726, 899}, {908, 3006}, {1265, 3436}, {3159, 3293}

▸ Functional Relations10 relations

• X₃₉₅₂ = isogonal conjugate of X₃₇₃₃

• X₃₉₅₂ = isotomic conjugate of X₇₁₉₂

• X₃₉₅₂ = complement of X₁₇₁₅₄

• X₃₉₅₂ = anticomplement of X₂₄₄

• X₃₉₅₂ = trilinear pole of line X₁₀X₃₇ (the tangent to Kiepert hyperbola at X₁₀, and the line of the degenerate cross-triangle of Gemini triangles 15 and 16)

• X₃₉₅₂ = X₅₂₃-cross conjugate of X₁₀

• X₃₉₅₂ = perspector of ABC and side-triangle of Gemini triangles 17 and 18

• X₃₉₅₂ = barycentric product of vertices of Gemini triangle 17

• X₃₉₅₂ = barycentric product of vertices of Gemini triangle 18

• X₃₉₅₂ = intersection, other than A, B, C, of {ABC, Gemini 17}-circumconic and {ABC, Gemini 18}-circumconic