I'm not sure I see what is the problem. You have two lines that intersect in a known point.
Solve for the equation of a circle (with known radius) that is tangent to both lines. All that is unknown are the coordinates of the center of that circle. In fact, you even can compute a line that must pass through that center point.
As simply, there is a basic formula for the distance to a line from a point . If the radius of the circle is given as r, then the point (x0,y0) must lie at a distance r from the line. Since you have two such lines, this is again a simple problem to solve.
Just sit down with a pencil and paper, and do a little basic algebra. Yeah, I know, you want me to do it for you. But the symbolic toolbox can do it easily enough.
