Paul's method, with an addendum, will give you what you want. It isn't as good as Visio's approach, but it is still quite doable.
Create a circle with the radius you desire, and use that as a template. Make that circle have a transparent center, and give it a thin outside thickness. Place the circle tangent to both lines. Then select the original line, and using the shape editor tool, create the new nodes, delete the center node, and drag the center of the new connecting line until it overlaps the arc of the circle.
Then drag the circle to the next intersection, and repeat. It will look machine-done in the end.
David
ps - when moving the circle, you can use the 'Alt' key and the arrow keys, to move the circle in very small increments, which makes final placement of the circle pretty easy.
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