{"app":{"locale":"en-GB"},"problem":{"content":"

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.

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