# Problem 562: Maximal perimeter
Construct triangle ABC such that: Vertices A, B and C are lattice points
inside or on the circle of radius r centered at the origin; the triangle
contains no other lattice point inside or on its edges; the perimeter is
maximum.Let R be the circumradius of triangle ABC and T(r) = R/r. For r
= 5, one possible triangle has vertices (-4,-3), (4,2) and (1,0) with
perimeter \$\\sqrt{13}+\\sqrt{34}+\\sqrt{89}\$ and circumradius R =
\$\\sqrt {\\frac {19669} 2 }\$, so T(5) =\$\\sqrt {\\frac {19669} {50}
}\$. You are given T(10) \~ 97.26729 and T(100) \~ 9157.64707. Find
T(107). Give your answer rounded to the nearest integer.