I am tackling a problem very similar to Calculate center of circle tangent to two lines in space. In fact I use the response from @ja72 to create a circle tangent to two existing lines. Works great.
Right now my radius is 4500 units. I know the segment lengths and the angle between them. There has to be a way I can determine the min/max radii that would satisfy tangency to the two segments without going outside their bounds. I just cant seem to wrap my head around the math.
Would the max radius be d*tan(α/2)? Where d is the smaller segment length.