Illustrator is for most intents and purposes a direct modeller. It does things as you would do on paper so for most parts you will be doing things manually. There are software that take a constraints based approach mostly only mechanical engineers use this kind of drawing tools (each industry has its own set of solutions to same problems, and those are alien to other industries).
In this case though the problem is pretty trivial. Recognize that the family of circles that are tangent to blue lines lie on a line that sits half way between the blue lines. Constructing this line can be done by 3 uses of circle tool, or 2 uses of rotate tool (rotate then numeric rotate half back). Or you can just offset teh lines and find the intersection
Image 1: Solution lies on the halfway line and green line intersection
But yeah tools that do this exist outside of graphic design try Geogebra or SolveSpace.