what these guys said
If for some reason you need 1/200th in this situation you could just take a step back and then crop the frame a bit to remove the edge. OR you can fiddle with trigger timing, or you could just lower the ambient some and you won't need 1/200th.
I also think a shutter synch speed of 1/200th is a bunch of hoohaa! i want 1/500th.
also, i don't think this is the problem here, but depending on what lighting gear you are using you could possibly be coming up against the flash duration. I think that(flash duration and how it would come into play) and the lack of people asking for it, mostly cause they don't understand it, are the causes for us still having crappy flash synch speeds.