X₁₇₁₂

MIMOSA TRANSFORM OF (20)

X₁₇₁₂ = eigencenter of cevian triangle of X₆₃

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

X₁₇₁₂ (MIMOSA TRANSFORM OF (20)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Cevian Triangle △P_aP_bP_c — vertices P_a, P_b, P_c (Traces of cevians through target center on BC, CA, AB)

• Concurrence Lines: A–P_a, B–P_b, C–P_c concurring at X₁₇₁₂

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X₂₀

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(0.861549113862\)

▸ Incident Central Lines15 lines

{1, 204}, {4, 57}, {9, 1249}, {19, 158}, {63, 1895}, {108, 1490}, {412, 1445}, {774, 1096}, {811, 1102}, {920, 1784}, {1103, 1783}, {1158, 1767}, {1708, 1715}, {1713, 1741}, {1714, 1728}

▸ Functional Relations4 relations

• X₁₇₁₂ = X_i-Ceva conjugate of X_j for these (i,j): (63, 19), (1895, 1)

• X₁₇₁₂ = X_i-aleph conjugate of X_j for these (i,j): (2, 2184), (1895, 1712)

• X₁₇₁₂ = eigencenter of cevian triangle of X₆₃

• X₁₇₁₂ = eigencenter of anticevian triangle of X₁₉