Greetings Everyone,

I was doing the maximum enclosing circle problem, This is the subproblem of that.

Given two ends points of a common chord of two circles of equal radius say R find out the coordinates of two centers of the circles (without much precision loss preferably)

The condition can be pictorially represented like.

A possible solution might be to find the coordinates of mid point of A and B that is M which is

Since the slope of line joining A and B is and since the line joining the centers would be perpendicular to the slope of line joining C1 and C2 would be .

The distance between the points M and C1 or C2 can be found using pythagoras theorem i.e. where

Now since we know the slope of the line and a point on it and distance between the points we can now find the coordinates of centers, but It's highly insensitive to precision.

Any other method, resource , links etc would be deeply appreciated.

Thanks in advance.