## Maximal perimeter

### Problem 562

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(10^{7}). Give your answer rounded to the nearest integer.