Assuming you are just going to tile a simple circle with a radius of 7', the calculation is easy to estimate number of tiles.
πR2 = Area
I'm going to use inches here: Radius is 84" = surface area of 22,156" squared.
It wouldn't be out of the question to calculate the number of tiles out of this, and add in a percentage for breakage/cuts. based on a 12" tile and 1/4" grout, I'd guess 150 tiles + 20% breakage/waste, or 177 tiles.
The next part gets more complicated. What I believe you're suggesting is cutting trapezoidal sections of tile, and arrange them in concentric rings. If you want to maximize the tile size, the pitch will be the same, but will not have the same layout on each and every tile. For each consecutive ring of tiles form the center, they will become more oblique and large.
I suggest doing an accurate scaled drawing in the spirit of what I threw together. Using autocad or sketchup would be highly advisable to make a 2D drawing. This is really the easiest way in my mind. Then you can have a firm plan of cuts, measurable angles, as well as a count of tiles.
Keep in mind, this is just about layout and measurements. I have NO idea of the tiles cut like this will be stable or if it will be easy to install.
Take your time, measure twice, cut once and when in doubt, step away and ask yourself "Is this work going to be worth the outcome".
Good luck and let us know how it goes!