X₁₆₁

X₆₃-OF-TANGENTIAL-TRIANGLE

X₁₆₁ = X₆₃-of-tangential triangle if ABC is acute

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

X₁₆₁ (X₆₃-OF-TANGENTIAL-TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {6, 25}, {26, 68}

• Related Centers: X₆₈ (PRASOLOV POINT), X₆ (SYMMEDIAN POINT), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₂₆ (CIRCUMCENTER OF THE TANGENTIAL TRIANGLE)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a[(a^{2} + b^{2} + c^{2})\sin^{2}(2A) + (c^{2} - b^{2} - a^{2})\sin^{2}(2B) + (b^{2} - c^{2} - a^{2})\sin^{2}(2C)]\)

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): \(6.599863926710\)

▸ Incident Central Lines4 lines

{6, 25}, {22, 343}, {26, 68}, {157, 418}

▸ Functional Relations2 relations

• X₁₆₁ = X₆₃-of-tangential triangle if ABC is acute

• X₁₆₁ = X₆₈-Ceva conjugate of X₆