Angry cows (january 2016 gold version)

I get that you should binary search the radius, but how do you go through all the possible positions to explode the cow at? You can’t cycle through all 2 billion possibilities (assuming you go to every 0.5 since cows can only be placed at integer points). If anyone could give a hint that would be helpful, i’m trying to avoid reading the whole editorial.

Why not binary search on the position as well?