[![problem](https://i.stack.imgur.com/8DlVp.png)](https://i.stack.imgur.com/8DlVp.png)

I want to calculate the circumcircle of three disks (center points is on grid points) in programming. Actually I already have a function to calculate circumcircle(s) of three disks but this function solves general-conditioned problems and a little slow (we use Mobius transform theory).

In my recent works, computation time is critical issue, and therefore I need a fast algorithm or equation of r\_1, r\_2, and r\_3 to calculate the center point and radius of circumcircle.

All disk triplets have center points (0, 0), (0, 1), and (1, 0), and their radii are d\_1, d\_2, and d\_3 respectively. Radii can be different and also same.