If I read the question correctly, you are constructing a triangle.
This is the geometer's method for constructing a triange when given the dimensions of three sides.
One of my first adventures into programming involved triangles and their construction. Its not quite what you are looking for, but on my web site (link in my signature) is a CorelScript program for Triangle Construction in Corel Draw that will draw a triange given
the dimensions of three sides (in your case the Base AB, the radius of the first circle, the radius of the second circle) also called SSS
or an Angle subtended by two known sides also called SAS
or any two angles and one side also called AAS
Also during my investigations I came across a program called The Geometer's Sketchpad that you might find interesting.
HTH
Peter
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