Hi,
I am not quite sure what exactly you want, but this involves a piecewise function of the equation of circles:
Plot[Piecewise[{{Sqrt[1 - x^2], x < 1}, {Sqrt[1 - (x - 2)^2], x > 1}}], {x, -1, 3}, AspectRatio -> 1/4]
This one also might be a possible answer:
ParametricPlot[Piecewise[{{{Cos[u], Sin[u]}, u < 2 Pi}, {{Cos[u] + 2., Sin[u] + 2.},u > 2 Pi}}], {u, 0, 4 Pi}]
Note that Piecewise has this form
so it does not actually have a slot for the equations for a circle. It needs the values in the form of a function.
Hope this helps,
M.