Minimise it

Let A, B, C be the three lattice points inside x² + y² = R² circle such that the ratio (c-a) / (a+b+c), where a = |BC|, b = |AC|, c = |AB| and a ≤ b ≤ c, is minimised. Solve it for R = 10⁹. Answer format: a²,b²,c² where gcd(a²,b²,c²) = 1 Example: 12544,12545,12545 for R=100 with ratio=1.328594679505981331113438939E-5 A(57,6), B(-40,-50), C(-40,62) [My timing: 200ms]