AutoCAD 2013 :: Is There A Chord Placement Option

The above image is the closest description of what I mean by a "chord" setting.  I need to be able to place lines with a specific length and orientation at a certian radius from two nonparallell curved lines. I've been finding it extremely difficult.

The blue lines are the property lines and the circles are the setbacks (hypothetically). To simplify the problem I offset the blue lines by the setback like so. which brigs me to the original problem. I need to place the building at the optimal point. So far, I have only been able to  get close and I know/think there should be a better method to solve my problem. In the example I provided, I knew exactly where the building should be placed because the offsets were the last thing I drew.  How can I get this result if my drawing is composed of fully drawn but nonaligned components?